JEE Main & Advanced Physics Rotational Motion Question Bank

done Mock Test - Centre of Mass, Conservation of Linear Momentum and Collisions Total Questions - 25

• question_answer1)
  A bag (mass \[M\]) hangs by a long thread and a bullet (mass \[m\]) comes horizontally with velocity \[v\] and gets caught in the bag. Then for the combined (bag + bullet) system
  A)
  Momentum is \[\frac{mvM}{M+m}\] done clear
  B)
   Kinetic energy is \[\frac{m{{v}^{2}}}{2}\] done clear
  C)
   Momentum is \[\frac{mv{{(M+m)}^{{}}}}{M}\] done clear
  D)
   Kinetic energy is \[\frac{{{m}^{2}}{{v}^{2}}}{2(M+m)}\] done clear
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• question_answer2)
  A free body of mass 8 kg is travelling at 2 meter per second in a straight line. At a certain instant, the body splits into two equal parts due to internal explosion which releases 16 joules of energy. Neither part leaves the original line of motion finally
  A)
  Both parts continue to move in the same direction as that of the original body done clear
  B)
   One part comes to rest and the other moves in the same direction as that of the original body done clear
  C)
   One part comes to rest and the other moves in the direction opposite to that of the original body done clear
  D)
   One part moves in the same direction and the other in the direction opposite to that of the original body done clear
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• question_answer3)
  Three particles of masses 1 kg, 2 kg and 3 kg are situated at the comers of an equilateral triangle move at speed \[6\,m{{s}^{-1}}\], \[3\,m{{s}^{-1}}\] and \[2\,m{{s}^{-1}}\] respectively. Each particle  maintains a direction towards the particle at the next comer symmetrically. Find velocity of CM of the system at this 2kg 4 instant
  A)
  \[3\,m{{s}^{-1}}\]                   done clear
  B)
  \[5\,m{{s}^{-1}}\] done clear
  C)
  \[6\,m{{s}^{-1}}\]       done clear
  D)
  Zero done clear
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• question_answer4)
  Two particles \[A\] and \[B\] start moving due to their mutual interaction only. If at any time\[t\], \[{{\vec{a}}_{A}}and\,{{\vec{a}}_{B}}\] are their respective accelerations, \[{{\vec{v}}_{A}}\,and\,{{\vec{v}}_{B}}\] are their respective velocities, and up to that time \[{{W}_{A\,}}and\,{{W}_{B}}\] are the work done on \[A\] and \[B\] respectively by the mutual force, \[{{m}_{A\,}}and\,{{m}_{B}}\] are their masses respectively, then which of the following is always correct?
  A)
  \[{{\vec{v}}_{A}}\,+\,{{\vec{v}}_{B}}=0\]     done clear
  B)
  \[{{m}_{A\,}}{{\vec{v}}_{A}}+\,{{m}_{B}}{{\vec{v}}_{B}}=0\] done clear
  C)
  \[{{W}_{A}}\,+\,{{W}_{B}}=0\]         done clear
  D)
  \[{{\vec{a}}_{A}}+{{\vec{a}}_{B}}=0\] done clear
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• question_answer5)
  The centre of mass of a non-uniform rod of length \[L\] whose mass per unit length \[\lambda \] varies as \[\lambda =\frac{k.{{x}^{2}}}{L}\]where k is a constant and x is the distance of any point on rod from its one end, is (from the same end)
  A)
  \[\frac{3}{4}L\] done clear
  B)
  \[\frac{1}{4}L\] done clear
  C)
  \[\frac{k}{L}\]              done clear
  D)
  \[\frac{3k}{L}\] done clear
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• question_answer6)
  In a system of particles 8 kg mass is subjected to a force of 16 N along \[+ve\,x-axis\] and another 8 kg mass is subjected to a force of 8 N along \[+ve\,y-axis\]. The magnitude of acceleration of centre of mass and the angle made by it with \[x-axis\] are given respectively by
  A)
  \[\frac{\sqrt{5}}{2}m{{s}^{-2}},\theta ={{45}^{0}}\] done clear
  B)
  \[3\sqrt{5}\,m{{s}^{-2}},\theta ={{\tan }^{-1}}(2/3)\] done clear
  C)
  \[\frac{\sqrt{5}}{2}\,m{{s}^{-2}},\theta ={{\tan }^{-1}}(1/2)\] done clear
  D)
  \[1\,m{{s}^{-2}},\theta ={{\tan }^{-1}}\sqrt{3}\] done clear
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• question_answer7)
  In a gravity free space, a man of mass \[M\] standing at a height \[h\] above the floor, throws a ball of mass m straight down with a speed \[u\]. When the ball reaches the floor, the distance of the man above the floor will be
  A)
   \[h(1+m/M)\] done clear
  B)
   \[h(2-m/M)\] done clear
  C)
   \[2h\] done clear
  D)
   a function of \[m\], \[M\], \[h\] and \[u\] done clear
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• question_answer8)
  The velocities of two particles \[A\] and \[B\] of same mass are \[{{\vec{V}}_{A}}=a\vec{i}\,and\,{{\vec{V}}_{B}}=b\hat{j}\] where a and b are constants. The acceleration of particle\[A\] is \[(2a\hat{i}+4b\hat{j})\] and acceleration of particle \[B\] is \[(a\hat{i}-4b\hat{j})\] (in \[m/{{s}^{2}}\]). The centre of mass of two particle will move in
  A)
  straight line        done clear
  B)
  parabola done clear
  C)
  ellipse   done clear
  D)
  circle done clear
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• question_answer9)
  A bar of mass \['m'\] length \[\ell \] is pure translator motion with its centre velocity \[v\]. It collides with another identical bar which is in rest and sticks to it. Assume that after the collision it becomes one system, then the angular velocity of the system after the collision is
  A)
  \[\frac{1}{5}\frac{v}{\ell }\]                  done clear
  B)
  \[\frac{2}{5}\frac{v}{\ell }\] done clear
  C)
  \[\frac{3}{5}\frac{v}{\ell }\]                  done clear
  D)
  \[\frac{v}{\ell }\] done clear
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• question_answer10)
  An object of mass 3m splits into three equal fragments. Two fragments have velocities \[v\hat{j}\,and\,v\hat{i}\]. The velocity of the third fragment is
  A)
   \[v(\hat{j}-\hat{i})\]       done clear
  B)
          \[v(\hat{i}-\hat{j})\] done clear
  C)
   \[-v(\hat{i}+\hat{j})\]    done clear
  D)
          \[\frac{v(\hat{i}+\hat{j})}{\sqrt{2}}\] done clear
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• question_answer11)
  Distance of the centre of mass of a solid uniform cone from its vertex is \[{{z}_{0}}\]. If the radius of its base is R and its height is h then \[{{z}_{0}}\] is equal to
  A)
  \[\frac{{{h}^{2}}}{4R}\]         done clear
  B)
  \[\frac{3{{h}^{{}}}}{4}\] done clear
  C)
  \[\frac{5{{h}^{{}}}}{8}\]                   done clear
  D)
  \[\frac{3{{h}^{2}}}{8R}\] done clear
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• question_answer12)
  Two objects that are moving along an \[xy\]-plane on a frictionless floor collide. Assume that they form a closed, isolated system. The following table gives some of the momentum components (in kilogram meters per second) before and after the collision. Before collision After collision

  	Before collision		After collision
  Object	\[{{p}_{x}}\]	\[{{p}_{Y}}\]	\[{{p}_{x}}\]	\[{{p}_{Y}}\]
  A	-4	5	3	A
  B	b	-2	4	2

  What are the missing values (a, b)?
  A)
  10, 11   done clear
  B)
  1, 11    done clear
  C)
  5, 7                  done clear
  D)
  6, 4 done clear
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• question_answer13)
  A ball is projected in a direction inclined to the vertical and bounces on a smooth horizontal plane. The range of one rebound is\[R\]. If the coefficient of restitution is \[e\], then range of the next rebound is
  A)
  \[R'=eR\]          done clear
  B)
  \[R'={{e}^{2}}R\] done clear
  C)
  \[R'=\frac{R}{e}\]         done clear
  D)
  \[R'=R\] done clear
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• question_answer14)
  Three blocks are initially placed as shown in the figure. Block \[A\] has mass m and initial velocity \[v\] to the right. Block \[B\] with mass and block C with mass \[4m\] are both initially at rest. Neglect friction. All collisions are elastic. The final velocity of blocks \[A\] is
  A)
  0.6\[v\]to the left done clear
  B)
  1.4\[v\]to the left done clear
  C)
  \[v\] to the left   done clear
  D)
  0.4 \[v\] to the right done clear
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• question_answer15)
  A block of mass \[m\] starts from rest and slides down a frictionless semi-circular track from a height h as shown. When it reaches the lowest point of the track, it collides with a stationary piece of putty. also having mass m. If the block and the putty stick together and continue to slide, the maximum height that the block-putty system could reach is
  A)
   \[h\]/4               done clear
  B)
   \[h\]/2 done clear
  C)
   \[h\]                 done clear
  D)
   independent of \[h\] done clear
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• question_answer16)
  A ball falls vertically onto a floor with momentum \[p\], and then bounces repeatedly. If the coefficient of restitution is \[e\], then the total momentum imparted by the ball on the floor till the ball comes to rest is
  A)
   \[p(1+e)\]                     done clear
  B)
   \[\frac{p}{1-e}\] done clear
  C)
   \[p\left( 1+\frac{1}{e} \right)\]                done clear
  D)
   \[p\left( \frac{1+e}{1-e} \right)\] done clear
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• question_answer17)
  A ball collides with a fixed inclined plane of inclination \[\theta \]after falling through a distance\[h\]? If it moves horizontally just after the impact, the coefficient of restitution is
  A)
  \[\tan \,\theta \]  done clear
  B)
  \[{{\tan }^{2}}\,\theta \] done clear
  C)
   \[{{\cot }^{{}}}\,\theta \]         done clear
  D)
  \[{{\cot }^{2}}\,\theta \] done clear
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• question_answer18)
  A machinist starts with three identical square plates but cuts one comer from one of them, two comers from the second and three comers from the third. Rank the three according to the x-coordinate of their centre of mass, from smallest to largest.
  A)
  3, 1, 2   done clear
  B)
  1, 3, 2 done clear
  C)
  3, 2, 1  done clear
  D)
  1 and 3 tie, then 2 done clear
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• question_answer19)
  A mass m is rest on an inclined plane of mass M which is further resting on a smooth horizontal plane. Now  if the mass starts moving the position of C.M. of mass of system will
  A)
  remains unchanged done clear
  B)
   change along the horizontal done clear
  C)
   will move up in the vertical direction done clear
  D)
   will move down in the vertical direction and changes along the horizontal done clear
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• question_answer20)
  A ball kept in a closed box moves in the box making collisions with the walls. The box is kept on a smooth surface. The velocity of the centre of mass
  A)
  of the box remains constant done clear
  B)
   of the (box + ball), system remains constant done clear
  C)
   of the ball remains constant done clear
  D)
   of the ball relative to the box remains constant done clear
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• question_answer21)
  A body of mass 5 kg explodes at rest into three fragments with masses in the ratio 1:1:3. The fragments with equal masses fly in mutually perpendicular directions with speeds of 21 m/s. What is the velocity (in m/s) of the heaviest fragment?
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• question_answer22)
  Figure shows a cubical box that has been constructed from uniform metal plate of negligible thickness. The box is open at the top and has edge length 40 cm. The z co-ordinate of the centre of mass of the box in cm, is ___.
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• question_answer23)
  A highly elastic ball moving at a speed of 3 m/s approaches a wall moving towards it with a speed of 3 m/s. After the collision, what is the speed (in m/s) of the ball?
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• question_answer24)
  A ball impinges directly on another ball at rest. The first ball is brought to rest by the impact. If half of the kinetic energy is lost by the impact, the value of coefficient of restitution is _______.
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• question_answer25)
  Two particles of equal masses moving with same speed collide perfectly inelastically. After the collision the combined mass moves with half of the speed of the individual masses. What is the angle (in degree) between the initial momenta of individual particle?
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