Rotational Motion

This chapter has

Rotational Motion — solved practice questions

8 JEE Physics questions with step-by-step solutions. Attempt each, then reveal the answer.

1. Q1easy

   The moment of inertia of a uniform solid sphere of mass M and radius R about a diameter is:

   • A(1/2)MR^2
   • B(2/5)MR^2
   • CMR^2
   • D(2/3)MR^2
   Show answer & solution

   Correct answer: (B) (2/5)MR^2

   The standard result for a solid sphere about a diameter is I = (2/5)MR^2.

2. Q2medium

   A solid sphere rolls without slipping down an incline of angle 30 degrees (g = 10 m/s^2). Its linear acceleration is:

   • A5 m/s^2
   • B2.5 m/s^2
   • C25/7 m/s^2
   • D10 m/s^2
   Show answer & solution

   Correct answer: (C) 25/7 m/s^2

   For rolling without slipping, a = g sin(theta)/(1 + I/MR^2) = 10*0.5/(1 + 2/5) = 5/1.4 = 25/7 = 3.57 m/s^2.

3. Q3medium

   A solid sphere rolls without slipping. The fraction of its total kinetic energy that is rotational is:

   • A2/7
   • B5/7
   • C1/2
   • D1/3
   Show answer & solution

   Correct answer: (A) 2/7

   Rotational KE = (1/2)(2/5 MR^2)(v/R)^2 = (1/5)Mv^2 and total = (7/10)Mv^2, so the fraction is (1/5)/(7/10) = 2/7.

4. Q4easy

   A ballet dancer spins with her arms outstretched. When she pulls her arms in, reducing her moment of inertia to half, her angular velocity:

   • Ahalves
   • Bstays the same
   • Cbecomes one-fourth
   • Ddoubles
   Show answer & solution

   Correct answer: (D) doubles

   With no external torque, angular momentum L = I*omega is conserved. Halving I doubles omega.

5. Q5easy

   A uniform disc of mass 2 kg and radius 0.5 m rotates about its central axis. Its moment of inertia is:

   • A0.5 kg m^2
   • B0.25 kg m^2
   • C1 kg m^2
   • D0.125 kg m^2
   Show answer & solution

   Correct answer: (B) 0.25 kg m^2

   For a disc about its central axis, I = (1/2)MR^2 = (1/2)(2)(0.5)^2 = 0.25 kg m^2.

6. Q6medium

   A flywheel starts from rest and gains angular speed under a constant angular acceleration of 2 rad/s^2. The angle turned through in the first 5 s is:

   • A10 rad
   • B50 rad
   • C25 rad
   • D5 rad
   Show answer & solution

   Correct answer: (C) 25 rad

   theta = omega0*t + (1/2)*alpha*t^2 = 0 + (1/2)(2)(25) = 25 rad.

7. Q7easy

   Two point masses of 2 kg and 3 kg are placed at x = 0 and x = 5 m on a light rod. The centre of mass lies at:

   • A2.5 m
   • B2 m
   • C3.5 m
   • D3 m
   Show answer & solution

   Correct answer: (D) 3 m

   x_cm = (m1x1 + m2x2)/(m1 + m2) = (2*0 + 3*5)/(2+3) = 15/5 = 3 m.

8. Q8medium

   A ring, a disc, and a solid sphere of the same mass and radius are released from rest at the top of the same incline and roll down without slipping. Which reaches the bottom first?

   • ASolid sphere
   • BDisc
   • CRing
   • DAll together
   Show answer & solution

   Correct answer: (A) Solid sphere

   Acceleration a = g sin(theta)/(1 + I/MR^2) is largest for the smallest I/MR^2. The solid sphere has 2/5, the smallest, so it arrives first.

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