JEE Main & Advanced Physics Rotational Motion Question Bank

done Self Evaluation Test - System of Particles Rotational Motion Total Questions - 100

• question_answer1)
  The mass per unit length of a non-uniform rod of length L varies as \[m=\lambda x\] where \[\lambda \] is constant. The centre of mass of the rod will be at:
  A)
  \[\frac{2}{3}L\] done clear
  B)
  \[\frac{3}{2}L\] done clear
  C)
  \[\frac{1}{2}L\] done clear
  D)
  \[\frac{4}{3}L\] done clear
  View Solution play_arrow

• question_answer2)
  A pulley fixed to the ceiling carries a string with blocks of mass m and 3 m attached to its ends. The masses of string and pulley are negligible. When the system is released, its centre of mass moves with what acceleration?
  A)
  0 done clear
  B)
  \[-g/4\] done clear
  C)
  \[g/2\]   done clear
  D)
  \[-g/2\] done clear
  View Solution play_arrow

• question_answer3)
  Three identical spheres, each of mass 1 kg are kept as shown in figure, touching each other, with their centres on a straight line. If their centres are marked P, Q, R respectively, the distance of centre of mass of the system from P is
  A)
  \[\frac{PQ+PR+QR}{3}\] done clear
  B)
  \[\frac{PQ+PR}{3}\] done clear
  C)
  \[\frac{PQ+QR}{3}\] done clear
  D)
  \[\frac{PR+QR}{3}\] done clear
  View Solution play_arrow

• question_answer4)
  Two spheres A and B of masses m and 2m and radii 2R and R respectively are placed in contact as shown. The COM of the system lies                        
  A)
  insider                 done clear
  B)
    insider             done clear
  C)
  at the point of contact    done clear
  D)
  None of these          done clear
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• question_answer5)
  A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass is K. If radius of the ball be R, then the fraction of total energy associated with its rotational energy will be
  A)
  \[\frac{{{K}^{2}}}{{{R}^{2}}}\] done clear
  B)
  \[\frac{{{K}^{2}}}{{{K}^{2}}+{{R}^{2}}}\] done clear
  C)
  \[\frac{{{R}^{2}}}{{{K}^{2}}+{{R}^{2}}}\] done clear
  D)
  \[\frac{{{K}^{2}}+{{R}^{2}}}{{{R}^{2}}}\] done clear
  View Solution play_arrow

• question_answer6)
  A hollow smooth uniform sphere A of mass m rolls without sliding on a smooth horizontal surface. It collides head on elastically with another stationary smooth solid sphere B of the same mass m and same radius. The ratio of kinetic energy of B to that of A just after the collision is
  A)
  1 : 1 done clear
  B)
  2 : 3 done clear
  C)
  3 : 2 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer7)
  A solid sphere, disc and solid cylinder all of the same mass and made of the same material are allowed to roll down (from rest) on an inclined plane, then             
  A)
  solid sphere reaches the bottom first done clear
  B)
  solid sphere reaches the bottom last done clear
  C)
  disc will reach the bottom first done clear
  D)
  all reach the bottom at the same time done clear
  View Solution play_arrow

• question_answer8)
  A solid cylinder of mass m & radius R rolls down inclined plane without slipping. The speed of C.M. when it reaches the bottom is   
  A)
  \[\sqrt{2gh}\] done clear
  B)
  \[\sqrt{4gh/3}\] done clear
  C)
  \[\sqrt{3/4gh}\] done clear
  D)
  \[\sqrt{4gh}\] done clear
  View Solution play_arrow

• question_answer9)
  The least coefficient of friction for an inclined plane inclined at angle a with horizontal in order that a solid cylinder will roll down without slipping is
  A)
  \[\frac{2}{3}\tan \alpha \] done clear
  B)
  \[\frac{2}{7}\tan \alpha \] done clear
  C)
  \[\tan \alpha \]  done clear
  D)
  \[\frac{5}{7}\tan \alpha \] done clear
  View Solution play_arrow

• question_answer10)
  An annular ring with inner and outer radii \[{{R}_{1}}\]and \[{{R}_{2}}\] is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring, \[\frac{{{F}_{1}}}{{{F}_{2}}}\] is
  A)
  \[{{\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)}^{2}}\] done clear
  B)
  \[\frac{{{R}_{2}}}{{{R}_{1}}}\] done clear
  C)
  \[\frac{{{R}_{1}}}{{{R}_{2}}}\] done clear
  D)
  1 done clear
  View Solution play_arrow

• question_answer11)
  There are some passengers inside a stationary railway compartment. The centre of mass of the compartment itself (without the passengers) is\[{{C}_{1}}\], while the centre of mass of the 'compartment plus passengers' system is\[{{C}_{2}}\]. If the passengers move about inside the compartment then
  A)
  Both \[{{C}_{1}}\] and \[{{C}_{2}}\] will move with respect to the ground done clear
  B)
  Neither \[{{C}_{1}}\] nor \[{{C}_{2}}\] will be stationary with respect to the ground done clear
  C)
  \[{{C}_{1}}\] Will move but \[{{C}_{2}}\] will be stationary with respect to the ground done clear
  D)
  \[{{C}_{2}}\] will move but \[{{C}_{1}}\] will be stationary with respect to the ground done clear
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• question_answer12)
  Three masses are placed on the x-axis: 300 g at origin, 500g at \[x=40\text{ }cm\]and 400g at\[x=70cm\]. The distance of the centre of mass from the origin is
  A)
  40cm done clear
  B)
  45cm done clear
  C)
  50cm done clear
  D)
  30cm done clear
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• question_answer13)
  A body A of mass M while falling vertically downwards under gravity breaks into two parts; f a body B of mass - M and a body C of mass - M. The canter of mass of bodies B and C taken together shifts compared to that of body A
  A)
  does not shift done clear
  B)
  depends on height of breaking done clear
  C)
  towards body B done clear
  D)
  towards body C done clear
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• question_answer14)
  A system consists of three particles, each of mass m and located at (l, 1), (2, 2) and (3, 3). The co- ordinates of the centre of mass are
  A)
  (1, 1) done clear
  B)
  (2, 2) done clear
  C)
  (3, 3) done clear
  D)
  (6, 6) done clear
  View Solution play_arrow

• question_answer15)
  Two bodies of masses 2 kg and 4 kg are moving with velocities 2 m/s and 10 m/s respectively along same direction. Then the velocity of their centre of mass will be
  A)
  8.1 m/s done clear
  B)
  7.3 m/s done clear
  C)
  6.4 m/s done clear
  D)
  5.3 m/s done clear
  View Solution play_arrow

• question_answer16)
  Four particles of masses   a \[{{m}_{1,}}\,{{m}_{2,\,}}{{m}_{3,\,}}and\,{{m}_{4,}}\]placed at the vertices A, B, C and D as respectively of a square shown. The COM of the system will lie at diagonal A C if
  A)
  \[{{m}_{1}}={{m}_{3}}\] done clear
  B)
  \[{{m}_{2}}={{m}_{4}}\] done clear
  C)
  \[{{m}_{1}}={{m}_{2}}\] done clear
  D)
  \[{{m}_{3}}={{m}_{4}}\] done clear
  View Solution play_arrow

• question_answer17)
  In the figure shown ABC is a uniform wire. If centre of mass of wire lies vertically below point A, then \[\frac{BC}{AB}\] Disclose to:     
  A)
   1.85 done clear
  B)
  1.5             done clear
  C)
   1.37 done clear
  D)
  3        done clear
  View Solution play_arrow

• question_answer18)
  A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of the discs coincide. The centre of mass of the new disc is a / R form the centre of the bigger disc. The value of a is
  A)
  1/4 done clear
  B)
  1/3   done clear
  C)
  1/2  done clear
  D)
  1/6 done clear
  View Solution play_arrow

• question_answer19)
  The centre of mass of three bodies each of mass 1 kg located at the points (0,0), (3,0) and (0,4) in the XY plane is
  A)
  \[\left( \frac{4}{3},1 \right)\] done clear
  B)
  \[\left( \frac{1}{3},\frac{2}{3} \right)\] done clear
  C)
  \[\left( \frac{1}{2},\frac{1}{2} \right)\] done clear
  D)
  \[\left( 1,\,\frac{4}{3} \right)\] done clear
  View Solution play_arrow

• question_answer20)
  Three identical rods are hinged at point A as shown. The angle made by rod AB with vertical is    
  A)
  \[{{\tan }^{-1}}\left( \frac{1}{\sqrt{3}} \right)\] done clear
  B)
  \[{{\tan }^{-1}}\left( \frac{3}{4} \right)\] done clear
  C)
  \[{{\tan }^{-1}}\left( 1 \right)\] done clear
  D)
  \[{{\tan }^{-1}}\left( \frac{4}{3} \right)\] done clear
  View Solution play_arrow

• question_answer21)
  A spool is pulled horizontally by two equal and opposite forces as shown in fig. Which of        Rough the following statements are correct?
  A)
  The centre of mass moves towards left done clear
  B)
  The centre of mass moves towards right done clear
  C)
  The centre of mass remains stationary done clear
  D)
  The net force about the centre of mass of the spool is zero done clear
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• question_answer22)
  A metal sheet 14 cm x 2 cm of uniform thickness is cut into two pieces of width 2 cm. The two pieces are joined and laid along XY plane as shown. The centre of mass has the coordinates  
  A)
  (1, 1) done clear
  B)
  (7/2, 7/2)             done clear
  C)
       (13/4, 9/4) done clear
  D)
  (12/7, 8/7)    done clear
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• question_answer23)
                            A rod PQ of mass M and length L is hinged at end R The rod is kept horizontal by a massless string tied to point Q as shown in figure. When string is cut, the initial angular acceleration of the rod is       
  A)
  g/L done clear
  B)
  2g/L done clear
  C)
  \[\frac{2g}{3L}\]            done clear
  D)
  \[\frac{3g}{2L}\] done clear
  View Solution play_arrow

• question_answer24)
  Two objects P and Q initially at rest move towards each other under mutual force of attraction. At the instant when the velocity of P is v and that of Q is 2v, the velocity of centre of mass of the system is
  A)
  v done clear
  B)
  3v    done clear
  C)
  2v done clear
  D)
  zero done clear
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• question_answer25)
  A uniform thin rod AB of length L has linear mass density\[\mu (x)=a+\frac{bx}{L}\], where x is measured from A. If the CM of the rod lies at a distance of \[\left( \frac{7}{12} \right)\]L from A, then a and b are related as :
  A)
  \[a=2b\] done clear
  B)
  \[2a=b\] done clear
  C)
  \[a=b\] done clear
  D)
  \[3a=2b\] done clear
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• question_answer26)
  \[(n-1)\] equal point masses each of mass m are placed at the vertices of a regular n-polygon. The vacant vertex has a position vector a with respect to the centre of the polygon. The position vector of centre of mass is
  A)
  \[-\frac{1}{(n-a)}a\] done clear
  B)
  \[\frac{a}{(n+1)}\] done clear
  C)
  \[\frac{a}{n}\] done clear
  D)
  \[\frac{n}{a+1}\] done clear
  View Solution play_arrow

• question_answer27)
  A right circular cone of base diameter 3 cm and height 6cm is cut from a solid cylinder of diameter 5cm and height 12cm. Find the position of CG of rest of the body.
  A)
  2.1 cm done clear
  B)
  6.3 cm done clear
  C)
  8.2 cm done clear
  D)
  5.3 cm done clear
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• question_answer28)
  A solid sphere of radius R is placed on a smooth horizontal surface. A horizontal force F is applied at height h from the lowest point. For the maximum acceleration of the centre of mass,
  A)
  \[h=R\]  done clear
  B)
  \[h=2R\] done clear
  C)
  \[h=0\] done clear
  D)
  The acceleration will be same whatever h maybe done clear
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• question_answer29)
  Two persons of masses 55 kg and 65 kg respectively, are at the opposite ends of a boat. The length of the boat is 3.0 m and weighs 100 kg. The 55 kg man walks up to the 65 kg man and sits with him. If the boat is in still water the centre of mass of the system shifts by:
  A)
  3.0m     done clear
  B)
  2.3m done clear
  C)
  zero       done clear
  D)
  0.75m done clear
  View Solution play_arrow

• question_answer30)
  A wheel rotates with a constant acceleration of 2.0 radian/sec2. If the wheel starts from rest, the number of revolutions it makes in the first ten seconds will be approximately
  A)
  8 done clear
  B)
  16    done clear
  C)
  24 done clear
  D)
  32 done clear
  View Solution play_arrow

• question_answer31)
  When a ceiling fan is switched off, its angular velocity falls to half while it makes 36 rotations. How many more rotations will it make before coming to rest?
  A)
  24 done clear
  B)
  36    done clear
  C)
  18 done clear
  D)
  12 done clear
  View Solution play_arrow

• question_answer32)
  A mass is revolving in a circle which is in the plane of paper. The direction of angular acceleration is
  A)
  upward the radius done clear
  B)
  towards the radius done clear
  C)
  tangential done clear
  D)
  at right angle to angular velocity done clear
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• question_answer33)
  In a bicycle, the radius of rear wheel is twice the radius of front wheel. It \[{{r}_{f}}\]and \[{{r}_{r}}\] are the radii and \[{{v}_{f}}\] and \[{{v}_{r}}\] are the speeds of topmost points of wheels then
  A)
  \[{{v}_{r}}=2{{v}_{f}}\] done clear
  B)
  \[{{v}_{f}}=2{{v}_{r}}\] done clear
  C)
  \[{{v}_{f}}={{v}_{r}}\] done clear
  D)
  \[{{v}_{f}}=4{{v}_{r}}\] done clear
  View Solution play_arrow

• question_answer34)
  A particle moving in a circular path has an angular momentum of L. If the frequency of rotation is halved, then its angular momentum becomes
  A)
  \[\frac{L}{2}\]  done clear
  B)
  L done clear
  C)
  \[\frac{L}{3}\] done clear
  D)
  \[\frac{L}{4}\] done clear
  View Solution play_arrow

• question_answer35)
  The instantaneous angular position of a point on a rotating wheel is given by the equation\[\theta (t)=2{{t}^{3}}-6{{t}^{2}}\]. The torque on the wheel becomes zero at
  A)
  \[t=1s\] done clear
  B)
  \[t=0.5s\] done clear
  C)
  \[t=0.25s\] done clear
  D)
  \[t=2s\] done clear
  View Solution play_arrow

• question_answer36)
  A particle of mass 2 kg is on a smooth horizontal table and moves in a circular path of radius 0.6 m. The height of the table from the ground is 0.8 m. If the angular speed of the particle is 12 rad \[{{s}^{-1}}\], the magnitude of its angular momentum about a point on the ground right under the centre of the circle is
  A)
  \[14.4\,kg\,{{m}^{2}}{{s}^{-1}}\] done clear
  B)
  \[8.64\,kg\,{{m}^{2}}{{s}^{-1}}\] done clear
  C)
  \[20.16\,kg\,{{m}^{2}}{{s}^{-1}}\] done clear
  D)
  \[11.52\,kg\,{{m}^{2}}{{s}^{-1}}\] done clear
  View Solution play_arrow

• question_answer37)
  If the angular momentum of a particle of mass m rotating along a circular path of radius r with uniform speed is L, the centripetal force acting on the particle is
  A)
  \[\frac{{{L}^{2}}}{m{{r}^{2}}}\] done clear
  B)
  \[\frac{{{L}^{2}}}{mr}\] done clear
  C)
  \[\frac{L}{mr}\] done clear
  D)
  \[\frac{{{L}^{2}}m}{r}\] done clear
  View Solution play_arrow

• question_answer38)
  Two particles which are initially at rest, move towards each other under the action of their internal attraction. If their speeds are v and 2v at any instant, then the speed of centre of mass of the system will be:
  A)
  2v done clear
  B)
  zero   done clear
  C)
   1.5 done clear
  D)
  v done clear
  View Solution play_arrow

• question_answer39)
  If the linear density (mass per unit length) of a rod of length 3m is proportional to x, where x is the distance from one end of the rod, the distance of the centre of gravity of the rod from this end is
  A)
  2.5m done clear
  B)
  1m  done clear
  C)
  1.5m done clear
  D)
  2m done clear
  View Solution play_arrow

• question_answer40)
  With 0 as the origin of the coordinate axis, the X and Y-coordinates of the centre of mass of the system of particles shown in the figure may be given as. Here m and 2m represent the masses of the particles.
  A)
  \[\left( -\frac{b}{2},0 \right)\] done clear
  B)
  \[\left( -\frac{b}{2},b \right)\] done clear
  C)
  \[\left( -\frac{b}{3},b \right)\] done clear
  D)
  \[\left( -\frac{b}{2}b,b \right)\] done clear
  View Solution play_arrow

• question_answer41)
  A thin bar of length L has a mass per unit length\[\lambda \], that increases linearly with distance from one end. If its total mass is M and its mass per unit length at the lighter end is\[{{\lambda }_{o}}\], then the distance of the centre of mass from the lighter end is:
  A)
  \[\frac{L}{2}-\frac{{{\lambda }_{o}}{{L}^{2}}}{4M}\]          done clear
  B)
         \[\frac{L}{3}+\frac{{{\lambda }_{o}}{{L}^{2}}}{8M}\] done clear
  C)
  \[\frac{L}{3}+\frac{{{\lambda }_{o}}{{L}^{2}}}{4M}\]           done clear
  D)
  \[\frac{2L}{3}+\frac{{{\lambda }_{o}}{{L}^{2}}}{6M}\] done clear
  View Solution play_arrow

• question_answer42)
  Two particles, each of mass 2 kg are put at (2m, 0) and (0, 2m), as shown in figure. Now 1 kg mass of particle A is put on to the particle B. The change in x-coordinate of centre of mass of the system is                    
  A)
  0.5m done clear
  B)
  1m                 done clear
  C)
  1.5m done clear
  D)
  None of these      done clear
  View Solution play_arrow

• question_answer43)
  Particles of masses m, 2m, 3m,.............nm grams are placed on the same line at distances \[l,\,2l,\,3l,\,.......nl\]cm from a fixed point. The distance of centre of mass of the particles from the fixed point in centimeters is
  A)
  \[\frac{(2n+1)l}{3}\] done clear
  B)
  \[\frac{1}{n+1}\] done clear
  C)
  \[\frac{n({{n}^{2}}+1)l}{2}\] done clear
  D)
  \[\frac{2l}{n({{n}^{2}}+1)}\] done clear
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• question_answer44)
  A wheel of radius 0.lm (wheel A) is attached by a non-stretching belt to a wheel of radius 0.2m (wheel B). The belt does not slip. By the time wheel B turns through 1 revolution, wheel A will rotate through               
  A)
  \[\frac{1}{2}\] revolution done clear
  B)
  1 revolution  done clear
  C)
  2 revolution done clear
  D)
  4 revolution done clear
  View Solution play_arrow

• question_answer45)
  The moment of inertia of a uniform circular disc of radius 'R' and mass 'M' about an axis passing from the edge of the disc and normal to the disc is
  A)
  \[M{{R}^{2}}\] done clear
  B)
  \[\frac{1}{2}M{{R}^{2}}\] done clear
  C)
  \[\frac{3}{2}M{{R}^{2}}\] done clear
  D)
  \[\frac{3}{2}M{{R}^{2}}\] done clear
  View Solution play_arrow

• question_answer46)
  Moment of inertia does not depend upon
  A)
  distribution of mass done clear
  B)
  axis of rotation done clear
  C)
  point of application of force done clear
  D)
  None of these done clear
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• question_answer47)
  Two identical discs of mass m and radius r are arranged as shown in the figure. If \[\alpha \] is the angular acceleration of the lower disc and \[{{a}_{cm}}\] is acceleration of centre of mass of the lower disc, then relation between  
  A)
  \[{{a}_{cm}}=\alpha /r\] done clear
  B)
  \[{{a}_{cm}}=2\alpha r\] done clear
  C)
  \[{{a}_{cm}}=\alpha r\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer48)
  A wheel having angular momentum \[2\pi \,kg-{{m}^{2}}/s\]about its vertical axis, rotates at the rate of 60 rpm about this axis. The torque which can stop the wheel's rotation in 30 sec would be
  A)
  \[\frac{\pi }{18}Nm\] done clear
  B)
  \[\frac{2\pi }{15}Nm\] done clear
  C)
  \[\frac{\pi }{12}Nm\] done clear
  D)
  \[\frac{\pi }{15}Nm\]      done clear
  View Solution play_arrow

• question_answer49)
  A wheel of radius 1 m rolls forward half are revolution on a horizontal ground. The magnitude of the displacement of the point of the wheel initially in contact with the ground is  
  A)
  \[\pi \] done clear
  B)
  \[2\pi \] done clear
  C)
  \[\sqrt{2\pi }\] done clear
  D)
  \[\sqrt{{{\pi }^{2}}+4}\] done clear
  View Solution play_arrow

• question_answer50)
  A sphere of mass ?m? is given some angular velocity   about   a horizontal axis through its centre and gently placed on a plank of mass ?m The coefficient of friction between the two is\[\mu \]. The plank rests on a smooth horizontal surface. The initial acceleration of the plank is
  A)
  Zero   done clear
  B)
         \[(7/5)\mu g\] done clear
  C)
  \[\mu g\]  done clear
  D)
  \[2\mu g\] done clear
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• question_answer51)
  Moment of inertia of a circular wire of mass M and radius R about its diameter is 
  A)
  \[M{{R}^{2}}/2\]  done clear
  B)
  \[M{{R}^{2}}\] done clear
  C)
  \[2M{{R}^{2}}\] done clear
  D)
  \[M{{R}^{2}}/4\] done clear
  View Solution play_arrow

• question_answer52)
  Moment of inertia of a hollow cylinder of mass M and radius r about its own axis is
  A)
  \[\frac{2}{3}M{{r}^{2}}\] done clear
  B)
  \[\frac{2}{5}M{{r}^{2}}\] done clear
  C)
  \[\frac{1}{3}M{{r}^{2}}\]  done clear
  D)
  \[M{{r}^{2}}\] done clear
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• question_answer53)
  Linear acceleration of hallow cylinder of mass \[{{m}_{2}}\]is \[{{a}_{2}}\]Then angular acceleration\[{{\alpha }_{2}}\] is (given that there is no slipping).           
  A)
  \[\frac{{{a}_{2}}}{R}\] done clear
  B)
  \[\frac{({{a}_{2}}+g)}{R}\] done clear
  C)
  \[\frac{2({{a}_{2}}+g)}{R}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer54)
  Which of the following has the highest moment of inertia when each of them has the same mass and the same outer radius
  A)
  a ring about its axis, perpendicular to the plane of the ring done clear
  B)
  a disc about its axis, perpendicular to the plane of the ring done clear
  C)
  a solid sphere about one of its diameters done clear
  D)
  a spherical shell about one of its diameters done clear
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• question_answer55)
  Radius of gyration of a body depends upon
  A)
  axis of rotation done clear
  B)
  translational motion done clear
  C)
  shape of the body done clear
  D)
  area of the body done clear
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• question_answer56)
  A and B are moving in 2 circular orbits with angular velocity   2\[\omega \]   and \[\omega \]respectively. Their positions are as shown at \[t=0\]. Find the time when they will meet for the first time.              
  A)
  \[\frac{\pi }{2\omega }\] done clear
  B)
  \[\frac{3\pi }{2\omega }\] done clear
  C)
  \[\frac{\pi }{\omega }\] done clear
  D)
  they will never meet done clear
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• question_answer57)
   If \[{{I}_{xy}}\]is the moment of inertia of a ring about a tangent in the plane of the ring and \[{{I}_{x'y'}}\] is the moment of inertia of a ring about a tangent perpendicular to the plane of the ring then
  A)
  \[{{I}_{xy}}={{I}_{x'y'}}\] done clear
  B)
  \[{{I}_{xy}}=\frac{1}{2}{{I}_{x'y'}}\] done clear
  C)
  \[{{I}_{x'y'}}=\frac{3}{4}{{I}_{xy}}\] done clear
  D)
  \[{{I}_{xy}}=\frac{3}{4}{{I}_{x'y'}}\] done clear
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• question_answer58)
  The moment of inertia of a uniform circular disc (figure) is maximum about an axis   a perpendicular to the disc and passing through                
  A)
  B done clear
  B)
  C          done clear
  C)
  D   done clear
  D)
  A done clear
  View Solution play_arrow

• question_answer59)
  One solid sphere A and another hollow sphere B are of same mass and same outer radii. Their moments of inertia about their diameters are respectively \[{{I}_{A}}\]and \[{{I}_{B}}\] such that Here \[{{\rho }_{A}}\]and \[{{\rho }_{B}}\]represent their densities.
  A)
  \[{{I}_{A}}={{I}_{B}}\]          done clear
  B)
  \[{{I}_{A}}>{{I}_{B}}\] done clear
  C)
  \[{{I}_{A}}<{{I}_{B}}\]           done clear
  D)
         \[{{I}_{A}}/{{I}_{B}}={{\rho }_{A}}={{\rho }_{B}}\] done clear
  View Solution play_arrow

• question_answer60)
  A wheel having moment of inertia \[2\,kg-{{m}^{2}}\] about its vertical axis, rotates at the rate of 60 rpm about this axis. The torque which can stop the wheel's rotation in one minute would be
  A)
  1.12Nm done clear
  B)
  0.83Nm done clear
  C)
  0.55Nm done clear
  D)
  0.21 Nm done clear
  View Solution play_arrow

• question_answer61)
  Three particles, each of mass m gram, are situated at the vertices of an equilateral triangle ABC of side f. cm (as shown in the figure). The moment of inertia of the system about a line AX perpendicular to AB and in the plane of ABC, in gram-cm2 units will be  
  A)
  \[\frac{3}{2}m{{\ell }^{2}}\]    done clear
  B)
  \[\frac{3}{4}m{{\ell }^{2}}\] done clear
  C)
  \[2m{{\ell }^{2}}\]       done clear
  D)
  \[\frac{5}{4}m{{\ell }^{2}}\] done clear
  View Solution play_arrow

• question_answer62)
  A round disc of moment of inertia \[{{I}_{2}}\]about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia \[{{I}_{1}}\]rotating with w angular velocity co about the same axis. The final angular velocity of the combination of discs is
  A)
  \[\frac{({{I}_{1}}+{{I}_{2}})\omega }{{{I}_{1}}}\]   done clear
  B)
  \[\frac{{{I}_{2}}\omega }{{{I}_{1}}+{{I}_{2}}}\] done clear
  C)
  \[\omega \] done clear
  D)
  \[\frac{{{I}_{1}}\omega }{{{I}_{1}}+{{I}_{2}}}\] done clear
  View Solution play_arrow

• question_answer63)
  The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the plane of the ring is
  A)
  \[1:\sqrt{2}\] done clear
  B)
  l : 3   done clear
  C)
  2: l    done clear
  D)
  \[\sqrt{5}:\sqrt{6}\] done clear
  View Solution play_arrow

• question_answer64)
  The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its midpoint and perpendicular to its length is\[{{I}_{0}}\]. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is
  A)
  \[{{I}_{0}}+M{{L}^{2}}/2\] done clear
  B)
  \[{{I}_{0}}+M{{L}^{2}}/4\] done clear
  C)
  \[{{I}_{0}}+2M{{L}^{2}}\] done clear
  D)
  \[{{I}_{0}}+M{{L}^{2}}\] done clear
  View Solution play_arrow

• question_answer65)
  The moment of inertia of the rectangular plate \[ABCD,(AB=2\text{ }BC)\]is minimum along the axis
  A)
  GH done clear
  B)
  EF done clear
  C)
  BC done clear
  D)
  AC               done clear
  View Solution play_arrow

• question_answer66)
              Four point masses, each of value m, are placed at the comers of a square ABCD of side \[\ell \].The moment of inertia of this system about an axis passing through A and parallel to BD is
  A)
  \[2m{{\ell }^{2}}\] done clear
  B)
  \[\sqrt{3}m{{\ell }^{2}}\] done clear
  C)
  \[3m{{\ell }^{2}}\] done clear
  D)
  \[m{{\ell }^{2}}\] done clear
  View Solution play_arrow

• question_answer67)
  Consider a uniform square plate of side 'a' and mass 'm'. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its comers is
  A)
  \[\frac{5}{6}m{{a}^{2}}\] done clear
  B)
  \[\frac{1}{12}m{{a}^{2}}\] done clear
  C)
  \[\frac{7}{12}m{{a}^{2}}\] done clear
  D)
  \[\frac{2}{3}m{{a}^{2}}\] done clear
  View Solution play_arrow

• question_answer68)
  Point masses 1, 2, 3 and 4 kg are lying at the points (0,0,0), (2,0,0), (0,3,0) and (-2, -2,0) respectively. The moment of inertia of this system about X-axis will be
  A)
  \[43\,kg\,{{m}^{2}}\] done clear
  B)
  \[34\,kg\,{{m}^{2}}\] done clear
  C)
  \[27\,kg\,{{m}^{2}}\] done clear
  D)
  \[72\,kg\,{{m}^{2}}\] done clear
  View Solution play_arrow

• question_answer69)
  The moment of inertia of a circular disc of mass and radius R about an axis passing through the centre of mass is\[{{I}_{0}}\]. The moment of inertia of another circular disc of same mass and thickness but half the density about the same axis is
  A)
   \[\frac{{{I}_{0}}}{8}\] done clear
  B)
  \[\frac{{{I}_{0}}}{4}\] done clear
  C)
  \[8{{I}_{0}}\] done clear
  D)
  \[2{{I}_{0}}\] done clear
  View Solution play_arrow

• question_answer70)
  A hollow sphere of mass 2 kg is kept on a rough horizontal surface. A force of 10 N is applied at the centre of the sphere as shown in the figure. Find the minimum value \[\mu \]so that the sphere starts pure rolling. (\[Take\,g=10m/{{s}^{2}}\])  
  A)
  \[\sqrt{3}\times 0.16\] done clear
  B)
  \[\sqrt{3}\times 0.08\] done clear
  C)
  \[\sqrt{3}\times 0.1\] done clear
  D)
  Data insufficient done clear
  View Solution play_arrow

• question_answer71)
  A sphere is spinned in a clockwise direction by   angular velocity \[\frac{{{V}_{0}}}{R}\]and then it is released to a rough surface. The time elapsed by the sphere, till it starts pure rolling (coefficient of friction is\[\mu \]) is [Radius of sphere is R].            
  A)
  \[\frac{2{{V}_{0}}}{7\mu g}\] done clear
  B)
  \[\frac{2{{V}_{0}}}{5\mu g}\] done clear
  C)
  \[\frac{3{{V}_{0}}}{5\mu g}\] done clear
  D)
  \[\frac{5{{V}_{0}}}{7\mu g}\] done clear
  View Solution play_arrow

• question_answer72)
  A cylinder A rolls without slipping on a plank B. The velocities of center of the cylinder and that of the plank are 4m/s and 2m/s respectively in same direction, with respect to the ground. Find the angular velocity of the cylinder (in rad/s) if its radius is 1m.
  A)
  2rad/sec done clear
  B)
  4rad/sec done clear
  C)
  6rad/sec done clear
  D)
  l0rad/sec done clear
  View Solution play_arrow

• question_answer73)
  A thick-walled hollow sphere has outside radius\[{{R}_{0}}\]. It rolls down an incline without slipping and its speed at the bottom is\[{{v}_{0}}\]. Now the incline is waxed, so that it is practically frictionless and the sphere is observed to slide down (without any rolling). Its speed at the bottom is observed to be\[5{{v}_{0}}/4\]. The radius of gyration of the hollow sphere about an axis through its centre is
  A)
  \[3{{R}_{0}}/2\] done clear
  B)
  \[3{{R}_{0}}/4\] done clear
  C)
  \[9{{R}_{0}}/16\] done clear
  D)
  \[3{{R}_{0}}\] done clear
  View Solution play_arrow

• question_answer74)
  Consider a thin uniform square sheet made of a rigid material. If its side is ?a? mass m and moment of inertia I about one of its diagonals, then
  A)
  \[I>\frac{m{{a}^{2}}}{12}\] done clear
  B)
  \[\frac{m{{a}^{2}}}{24}<I<\frac{m{{a}^{2}}}{12}\] done clear
  C)
  \[I=\frac{m{{a}^{2}}}{24}\] done clear
  D)
  \[I=\frac{m{{a}^{2}}}{12}\] done clear
  View Solution play_arrow

• question_answer75)
  From a solid sphere of mass M and radius R a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its center and perpendicular to one of its faces is
  A)
  \[\frac{4M{{R}^{2}}}{9\sqrt{3\pi }}\] done clear
  B)
  \[\frac{4M{{R}^{2}}}{3\sqrt{3\pi }}\] done clear
  C)
  \[\frac{M{{R}^{2}}}{32\sqrt{2\pi }}\] done clear
  D)
  \[\frac{M{{R}^{2}}}{16\sqrt{2\pi }}\] done clear
  View Solution play_arrow

• question_answer76)
  Two discs rotating about their respective axis of rotation with angular speeds\[2rad{{s}^{-1}}\] and\[5rad{{s}^{-1}}\] are brought into contact such that their axes of rotation coincide. Now, the angular speed of the system becomes\[4rad{{s}^{-1}}\]. If the moment of inertia of the second disc is\[1\times {{10}^{-3}}\text{ }kg\text{ }{{m}^{2}}\], then the moment of inertia of the first disc \[(in\text{ }kg\text{ }{{m}^{2}})\] is
  A)
  \[0.25\times {{10}^{-3}}\] done clear
  B)
  \[1.5\times {{10}^{-3}}\] done clear
  C)
  \[1.25\times {{10}^{-3}}\] done clear
  D)
  \[0.5\times {{10}^{-3}}\] done clear
  View Solution play_arrow

• question_answer77)
  Two bodies have their moments of inertia I and 21 respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momenta will be in the ratio
  A)
  2:1  done clear
  B)
  1:2   done clear
  C)
  \[\sqrt{2}:1\] done clear
  D)
  \[1:\sqrt{2}\] done clear
  View Solution play_arrow

• question_answer78)
  M.I of a circular loop of radius R about the axis in figure is                 
  A)
  \[M{{R}^{2}}\] done clear
  B)
  \[(3/4)M{{R}^{2}}\] done clear
  C)
  \[M{{R}^{2}}/2\] done clear
  D)
  \[2M{{R}^{2}}\] done clear
  View Solution play_arrow

• question_answer79)
  A rod of mass m and length \[l\] is bent in to mil shape of Z. Its moment of inertia about the axis         shown in figure                
  A)
   \[\frac{m{{l}^{2}}}{6}\] done clear
  B)
  \[\frac{m{{l}^{2}}}{3}\] done clear
  C)
  \[\frac{m{{l}^{2}}}{2}\] done clear
  D)
  None done clear
  View Solution play_arrow

• question_answer80)
  The moment of inertia of a hollow thick spherical shell of mass M and its inner radius \[{{R}_{1}}\] and outer radius \[{{R}_{2}}\] about its diameter is
  A)
  \[\frac{2M}{5}\frac{(R_{2}^{5}-R_{1}^{5})}{(R_{2}^{5}-R_{1}^{3})}\] done clear
  B)
  \[\frac{2M}{5}\frac{(R_{2}^{5}-R_{1}^{5})}{(R_{2}^{3}-R_{1}^{3})}\] done clear
  C)
  \[\frac{4M}{5}\frac{(R_{2}^{5}-R_{1}^{5})}{(R_{2}^{3}-R_{1}^{3})}\] done clear
  D)
  \[\frac{4M}{3}\frac{(R_{2}^{5}-R_{1}^{5})}{(R_{2}^{3}-R_{1}^{3})}\] done clear
  View Solution play_arrow

• question_answer81)
  The moment of inertia of a uniform semicircular wire of mass m and radius r, about an axis passing through its centre of mass and perpendicular to its plane is \[m{{r}^{2}}\left( 1-\frac{k}{{{\pi }^{2}}} \right)\]then find the value of k.
  A)
  2 done clear
  B)
  3      done clear
  C)
  4 done clear
  D)
  5 done clear
  View Solution play_arrow

• question_answer82)
  A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2 revolutions \[{{s}^{-2}}\]is
  A)
  25 N done clear
  B)
  50 N done clear
  C)
  78.5 N done clear
  D)
  157 N done clear
  View Solution play_arrow

• question_answer83)
  A child with mass m is standing at the edge of a playground merry-go-round (A large uniform disc which rotates in horizontal plane about a fixed vertical axis in parks) with moment of inertia Vs I, radius R, and initial angular velocity w as shown in the figure. The child jumps off the edge of the merry-go-round with a velocity v with respect to the ground in direction tangent to periphery of the disc as shown. The new angular veloity of the merry-go-round is :
  A)
  \[\sqrt{\frac{I{{\omega }^{2}}-m{{v}^{2}}}{I}}\] done clear
  B)
  \[\sqrt{\frac{(I+m{{R}^{2}}){{\omega }^{2}}-m{{v}^{2}}}{I}}\] done clear
  C)
  \[\frac{I\omega -mvR}{I}\] done clear
  D)
  \[\frac{(I\omega -m{{R}^{2}})\omega -mvR}{I}\] done clear
  View Solution play_arrow

• question_answer84)
    Two circular discs of same mass and thickness are made up of two different metals with densities \[{{d}_{x}}\]and\[{{d}_{Y}}({{d}_{X}}>{{d}_{Y}})\]. Their moments of inert about the axes passing through their centers of gravity and perpendicular to their planes are\[{{I}_{X}}\] and\[{{I}_{Y}}\]. Which one is correct?
  A)
  \[{{I}_{x}}>{{I}_{y}}\] done clear
  B)
  \[{{I}_{x}}<{{I}_{y}}\] done clear
  C)
  \[{{I}_{x}}={{I}_{y}}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer85)
  There is a flat uniform triangular A plate ABC such that \[AB=4cm,\text{ }BC=3cm\]and angle\[abc=90{}^\circ \]. The moment of inertia of the plate about AB, BC and CA as axis is respectively \[{{I}_{1,}}{{I}_{2}}\]and\[{{I}_{3}}\]. Which one of the following is true?     
  A)
  \[{{I}_{3}}>{{I}_{2}}\] done clear
  B)
  \[{{I}_{2}}>{{I}_{1}}\] done clear
  C)
  \[{{I}_{3}}>{{I}_{1}}\] done clear
  D)
  \[{{I}_{1}}>{{I}_{2}}\] done clear
  View Solution play_arrow

• question_answer86)
  The moment of inertia of a body about a given axis is\[1.2\text{ }kg\text{ }{{m}^{2}}\]. Initially, the body is at rest. In order to produce a rotational kinetic energy of 1500 joule, an angular acceleration of\[25radian/{{\sec }^{2}}\] must be applied about that axis for a duration of
  A)
  4 seconds done clear
  B)
  2 seconds done clear
  C)
  8 seconds done clear
  D)
  10 seconds done clear
  View Solution play_arrow

• question_answer87)
  A fly wheel rotating about a fixed axis has a kinetic energy of 360 joule when its angular speed is 30 radian/sec. The moment of inertia of the wheel about the axis of rotation is
  A)
  \[0.6kg/{{m}^{2}}\]        done clear
  B)
         \[0.15kg\,{{m}^{2}}\] done clear
  C)
  \[0.8kg\,{{m}^{2}}\]    done clear
  D)
  \[0.75kg\,{{m}^{2}}\] done clear
  View Solution play_arrow

• question_answer88)
  A bullet of mass 10 g and speed 500 m/s is fired into a door and gets embedded exactly at the centre of the door. The door is 1.0 m wide and weighs 12 kg. It is hinged at one end and rotates about a vertical axis practically without friction. The angular speed of the door just after the bullet embeds into it will be:
  A)
  6.25rad/sec       done clear
  B)
         0.625 rad/sec done clear
  C)
  3.35 rad/sec       done clear
  D)
         0.335 rad/sec done clear
  View Solution play_arrow

• question_answer89)
  A thin wire of length L and uniform linear mass density \[\rho \] is bent into a circular loop with centre at O as shown. The moment of inertia of the loop about the axis XX? is
  A)
  \[\frac{\rho {{L}^{3}}}{8{{\pi }^{2}}}\]         done clear
  B)
  \[\frac{\rho {{L}^{3}}}{16{{\pi }^{2}}}\] done clear
  C)
  \[\frac{5\rho {{L}^{3}}}{16{{\pi }^{2}}}\]      done clear
  D)
  \[\frac{3\rho {{L}^{3}}}{8{{\pi }^{2}}}\] done clear
  View Solution play_arrow

• question_answer90)
  A particle of mass m is attached to q a thin uniform rod of length a and mass 4 m. The distance of the particle from the centre of mass of the rod is a/4. The moment of inertia of the combination about an axis passing through 0 normal  to the rod is               
  A)
  \[\frac{64}{48}m{{a}^{2}}\] done clear
  B)
  \[\frac{91}{48}m{{a}^{2}}\] done clear
  C)
  \[\frac{27}{48}m{{a}^{2}}\] done clear
  D)
  \[\frac{51}{48}m{{a}^{2}}\] done clear
  View Solution play_arrow

• question_answer91)
  From a disc of radius R and mass M, a circular hole of diameter R, whose rim passes through the centre is cut. What is the radius of gyration of the remaining part of the disc about a perpendicular axis, passing through the centre?
  A)
  \[\frac{13}{2}R\] done clear
  B)
  \[\sqrt{\frac{13}{16}R}\] done clear
  C)
  \[\frac{11}{3}R\]   done clear
  D)
  \[\sqrt{\frac{13}{9}R}\] done clear
  View Solution play_arrow

• question_answer92)
  Four identical thin rods each of mass M and length\[l\], form a square frame. Moment of inertia of this frame about an axis through the centre of the square and perpendicular to its plane is :
  A)
  \[\frac{2}{3}M{{l}^{2}}\] done clear
  B)
  \[\frac{13}{3}M{{l}^{2}}\] done clear
  C)
  \[\frac{1}{3}M{{l}^{2}}\] done clear
  D)
  \[\frac{4}{3}M{{l}^{2}}\] done clear
  View Solution play_arrow

• question_answer93)
  From a circular disc of radius R and mass 9M, a   small disc of radius R/3 is removed from the disc. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through O is
  A)
  \[4M{{R}^{2}}\] done clear
  B)
  \[\frac{40}{9}M{{R}^{2}}\] done clear
  C)
  \[10M{{R}^{2}}\] done clear
  D)
  \[\frac{37}{9}M{{R}^{2}}\] done clear
  View Solution play_arrow

• question_answer94)
  A horizontal turn table in the form of a disc of radius r carries a gun at G and rotates with angular velocity \[{{\omega }_{0}}\] about a vertical axis passing through the centre O. The increase in angular velocity of the system if the gun fires a bullet of mass m with a tangential velocity v with respect to the gun is (moment of inertia of gun + table about 0 is \[{{I}_{0}}\])      
  A)
  \[\frac{mvr}{{{I}_{0}}+m{{r}^{2}}}\] done clear
  B)
  \[\frac{2mvr}{{{I}_{0}}}\] done clear
  C)
  \[\frac{v}{2r}\] done clear
  D)
  \[\frac{mvr}{2{{I}_{0}}}\] done clear
  View Solution play_arrow

• question_answer95)
  A tangential force of 20 N is applied on a cylinder of mass 4 kg and moment of    inertia \[0.02\,kg\,{{m}^{2}}\] about its own axis. If the cylinder rolls without slipping, then linear acceleration of its centre of mass will be
  A)
  \[6.7m/{{s}^{2}}\]          done clear
  B)
         \[10m/{{s}^{2}}\] done clear
  C)
  \[3.3m/{{s}^{2}}\]          done clear
  D)
         None of these done clear
  View Solution play_arrow

• question_answer96)
  A toy car rolls down the inclined plane as shown in the fig. It loops at the bottom. What is the relation between H and h? 
  A)
  \[\frac{H}{h}=2\]          done clear
  B)
  \[\frac{H}{h}=3\] done clear
  C)
  \[\frac{H}{h}=4\]          done clear
  D)
  \[\frac{H}{h}=5\] done clear
  View Solution play_arrow

• question_answer97)
  A thin ring, a disk and an annular cylinder, of same mass M, are released from a point 3.6m from the ground up an inclined plane of \[30{}^\circ \] degree inclination. The ring and the disk have the same radius R. Times taken by the ring and disk to reach the ground are in the ratio,
  A)
  \[\sqrt{2}:\sqrt{1.5}\]       done clear
  B)
         \[\sqrt{1.4}:\sqrt{1.5}\] done clear
  C)
  \[\sqrt{1.5}:\sqrt{1.5}\]     done clear
  D)
         \[\sqrt{1.5}:\sqrt{1.6}\] done clear
  View Solution play_arrow

• question_answer98)
  A rolling body is kept on a plank B. There is sufficient friction between A and B and no friction between B and the inclined plane. Then body :        
  A)
      A rolls done clear
  B)
  A does not experience any friction done clear
  C)
  A and B has equal acceleration and unequal velocities done clear
  D)
  A rolls depending upon the angle of inclination \[\theta \] done clear
  View Solution play_arrow

• question_answer99)
  In the figure shown mass of both, the spherical body and block is m. Moment of inertia of the spherical body about centre of mass is \[2m{{R}^{2}}\]. The spherical body rolls on the horizontal surface. There is no slipping at any surfaces in contact. The ratio of kinetic energy of the spherical body to that of block is
  A)
  3/4 done clear
  B)
  1/3    done clear
  C)
  2/3 done clear
  D)
  1/2 done clear
  View Solution play_arrow

• question_answer100)
  The free end of a thread wound on a bobbin is passed round a nail A hammered into the wall. The thread is pulled at a constant velocity. Assuming pure rolling of bobbin, find the velocity \[{{v}_{0}}\] of the centre of the bobbin at the instant when the thread forms an angle a with the vertical.
  A)
  \[\frac{vR}{R\sin \alpha -r}\] done clear
  B)
  \[\frac{vR}{R\sin \alpha +r}\] done clear
  C)
  \[\frac{2vR}{R\sin \alpha +r}\] done clear
  D)
  \[\frac{v}{R\sin \alpha +r}\] done clear
  View Solution play_arrow