JEE Main & Advanced Physics Rotational Motion Question Bank

done Mock Test - Dynamics of Rigid Body Total Questions - 25

• question_answer1)
  Three identical thin rods, each of length \[L\] and mass m, are welded perpendicular to one another as shown in figure. The assembly is rotated about an axis that passes through the end of one rod and is parallel to another. The moment of inertia of this structure about this axis is
  A)
  \[\frac{7}{12}m{{L}^{2}}\] done clear
  B)
  \[\frac{11}{14}m{{L}^{2}}\] done clear
  C)
  \[\frac{5}{15}m{{L}^{2}}\]    done clear
  D)
  \[\frac{11}{12}m{{L}^{2}}\] done clear
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• question_answer2)
  Three identical thin rods, each of mass \[m\] and length \[\ell \], are joined to form an equilateral triangular frame. The moment of inertia of the frame about an axis parallel to its one side and passing through the opposite vertex is
  A)
  \[\frac{5}{2}m{{\ell }^{2}}\]   done clear
  B)
  \[\frac{5}{4}m{{\ell }^{2}}\] done clear
  C)
  \[\frac{3}{2}m{{\ell }^{2}}\]   done clear
  D)
  \[\frac{5}{3}m{{\ell }^{2}}\] done clear
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• question_answer3)
  Which of the following has the highest moment of inertia when each of them has the same mass and the same radius?
  A)
  A ring about any of its diameter done clear
  B)
   A disc about any of its diameter done clear
  C)
   A hollow sphere about any of its diameter done clear
  D)
   A solid sphere about any of its diameter done clear
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• question_answer4)
  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 an axis XY is
  A)
  \[\frac{\rho {{L}^{3}}}{8{{\pi }^{2}}}\] done clear
  B)
  \[\frac{\rho {{L}^{3}}}{16{{\pi }^{2}}}\] done clear
  C)
  \[\frac{5\rho {{L}^{3}}}{8{{\pi }^{2}}}\] done clear
  D)
  \[\frac{3\rho {{L}^{3}}}{8{{\pi }^{2}}}\] done clear
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• question_answer5)
  Two points of a rod move with velocities 3\[v\] and perpendicular to the rod and in the same direction, separated by a distance 'r'. Then the angular velocity of the rod is
  A)
  \[\frac{3v}{r}\]             done clear
  B)
  \[\frac{4v}{r}\] done clear
  C)
  \[\frac{5v}{r}\]             done clear
  D)
  \[\frac{2v}{r}\] done clear
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• question_answer6)
  A hoop rolls on a horizontal ground without Slipping with linear speed \[v\]. Speed of a particle \[P\] on the circumference of the hoop at angle \[\theta \] is
  A)
  \[2v\,\sin \,(\theta /2)\]    done clear
  B)
  \[v\,\sin \,\theta \] done clear
  C)
  \[2v\,\cos \,(\theta /2)\]   done clear
  D)
  \[v\,\cos \,\theta \] done clear
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• question_answer7)
  A triangular set square of angles \[30{}^\circ ,\text{ }60{}^\circ ,\text{ }90{}^\circ \] and of negligible mass is suspended freely from the right angled comer and weights are hung at the two comers. If the hypotenuse of the set square sets horizontally, then the ratio of the weights \[{{W}_{1}}/{{W}_{2}}\] is
  A)
  \[1:1\]               done clear
  B)
  \[1:3\] done clear
  C)
  \[\sqrt{3}:1\]     done clear
  D)
  \[1:\sqrt{3}\] done clear
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• question_answer8)
  A thick walled hollow sphere has outer radius \[R\]. It rolls down an inclined plane without slipping and its speed at the bottom is\[v\]. If the inclined plane is frictionless and the sphere slides down without rolling, its speed at the bottom is \[5v/4\]. What is the radius of gyration of the sphere?
  A)
  \[\frac{R}{\sqrt{2}}\]                 done clear
  B)
  \[\frac{R}{2}\] done clear
  C)
  \[\frac{3R}{4}\]            done clear
  D)
  \[\frac{\sqrt{3}R}{4}\] done clear
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• question_answer9)
  A circular disc x of radius \[R\] is made from an iron plate of thickness \[t\], and another disc \[Y\] of radius 4\[R\] is made from an iron plate of thickness \[t\]/4. Then the relation between the moment of inertia \[{{I}_{x\,}}\,and\,{{I}_{Y}}\]is
  A)
  \[{{I}_{Y}}=64{{I}_{X}}\] done clear
  B)
  \[{{I}_{Y}}=32{{I}_{X}}\] done clear
  C)
  \[{{I}_{Y}}=16{{I}_{X}}\] done clear
  D)
  \[{{I}_{Y}}={{I}_{X}}\] done clear
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• question_answer10)
  A horizontal heavy uniform bar of weight \[W\] is supported at its ends by two men. At the instant, one of the men lets go off his end of the rod, the other feels the force on his hand changed to
  A)
  \[W\]                done clear
  B)
  \[\frac{W}{2}\] done clear
  C)
  \[\frac{3W}{4}\]                       done clear
  D)
  \[\frac{W}{4}\] done clear
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• question_answer11)
   A cube of side \[a\] is placed on an inclined plane of inclination \[\theta \]. What is the maximum value of 9 for which the cube will not topple?
  A)
  \[15{}^\circ \]              done clear
  B)
  \[30{}^\circ \]      done clear
  C)
  \[45{}^\circ \]  done clear
  D)
  \[69{}^\circ \] done clear
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• question_answer12)
  A uniform disc of mass \[M\] and radius \[R\] is mounted on an axle supported in frictionless bearings. A light cord is wrapped around the rim of the disc and a steady downward pull \[T\] is exerted on the cord. The angular acceleration of the disc is
  A)
  \[\frac{T}{MR}\]                       done clear
  B)
  \[\frac{MR}{T}\] done clear
  C)
  \[\frac{2T}{MR}\]         done clear
  D)
  \[\frac{MR}{2T}\] done clear
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• question_answer13)
  A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is K. The child now stretches his arms so that the moment of inertia of the system doubles. The kinetic energy of the system now is
  A)
  \[2K\]               done clear
  B)
  \[\frac{K}{2}\] done clear
  C)
  \[\frac{K}{4}\]              done clear
  D)
  \[4K\] done clear
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• question_answer14)
  Two points of a rod move with velocities \[3v\] and \[v\] perpendicular to the rod and in the same direction separated by a distance '\[r\]'. The angular velocity of the rod is
  A)
  \[\frac{3v}{r}\]             done clear
  B)
  \[\frac{4v}{r}\] done clear
  C)
  \[\frac{5v}{r}\]             done clear
  D)
  \[\frac{2v}{r}\] done clear
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• question_answer15)
  A particle is moving along a line \[y=x+a\] with a constant velocity \[v\]. Find the angular momentum of the particle about the origin.
  A)
  \[mva\] done clear
  B)
  \[mva\sqrt{2}\] done clear
  C)
  \[\frac{mva}{\sqrt{2}}\] done clear
  D)
  \[\frac{mvy}{x\sqrt{2}}\] done clear
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• question_answer16)
  A body is rolling without slipping on a horizontal plane. The rotational energy of the body is 40% of the total kinetic energy. Identify the body.
  A)
  Ring                  done clear
  B)
  Hollow cylinder done clear
  C)
  Solid cylinder    done clear
  D)
  Hollow sphere done clear
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• question_answer17)
  A small solid sphere of radius \[r\] rolls down an incline without slipping which ends into a vertical loop of radius \[R\]. Find the height above the base so that it just loops the loop
  A)
  \[\frac{5}{2}R\]            done clear
  B)
  \[\frac{5}{2}(R-r)\] done clear
  C)
  \[\frac{25}{10}(R-r)\]     done clear
  D)
  \[\frac{27}{10}R-\frac{17r}{10}\] done clear
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• question_answer18)
  A uniform rod of length \[L\] (in between the supports) and mass \[m\] is placed on two supports \[A\] and \[B\]. The rod breaks suddenly at length \[L/10\] from the support B. Find the reaction at support A immediately after the rod breaks.
  A)
  \[\frac{9}{40}mg\]        done clear
  B)
  \[\frac{19}{40}mg\] done clear
  C)
  \[\frac{mg}{2}\]                        done clear
  D)
  \[\frac{9}{20}mg\] done clear
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• question_answer19)
  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
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• question_answer20)
  A pulley of radius 2 m is rotated about its axis by a force \[F=(20t-5{{t}^{2}})\] newton (where \[t\] is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is \[10\,kg{{m}^{2}}\], the number of rotations made by the pulley before its direction of motion is reversed, is:
  A)
  less than 3 done clear
  B)
  more than 3 but less than 6 done clear
  C)
  more than 6 but less than 9 done clear
  D)
  more than 9 done clear
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• question_answer21)
  Particle P shown in figure is moving in a circle of radius \[R=10\] cm of with linear speed \[v\,=\,2m{{s}^{-1}}\].The angular speed of particle about a fixed point 0 on the circle is (in rad/s) ______.
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• question_answer22)
  The wheel in figure has eight equally spaced spokes and a radius of 30 cm. It is mounted on a fixed axle and is spinning at 2.5 rev/s. You want to shoot a 29-cm-long arrow parallel to this axle and through the wheel Without hitting any of the spokes. Assume that the arrow and the spokes are very thin. What minimum speed (in m/s) must the arrow have?
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• question_answer23)
  A uniform rod of mass 15 kg is held stationary with the help of a light string as shown in the figure. The tension in the string is (in N) _____.
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• question_answer24)
  Two discs, each having moment of inertia \[5\,kg\,{{m}^{2}}\] about its central axis, rotating with speeds 10 rad \[{{s}^{-1}}\] and 20 rad \[{{s}^{-1}}\], are brought in contact face to face with their axes of rotation coincided. The loss of kinetic energy in the process is (in J) ______ .
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• question_answer25)
  The moment of inertia of a uniform cylinder of length \[l\]and radius \[R\] about its perpendicular bisector is \[I\]. What is the ratio \[l\]\[/R\] such that the moment of inertia is minimum?
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