MHT CET202522 Apr 2025Evening ShiftPhysicsRotational MotionActual
A solid cylinder of mass ' M ' and radius ' R ' is rotating about its geometrical axis. A solid sphere of same mass and same radius is also rotating about its diameter with an angular speed half that of the cylinder. The ratio of the kinetic energy of rotation of the sphere to that of the cylinder will be
Options
- A2: 3
- B3: 2
- C1: 5
- D5: 1
Correct answer
C. 1: 5
Step-by-step solution
Kinetic energy ratio calculation Given a solid cylinder and solid sphere with equal mass M and radius R , where the cylinder rotates with angular speed and the sphere with /2 . The rotational kinetic energy ratio K_s K_c is determined. The moment of inertia for the cylinder about its axis is I_c = 1 2 MR^2 , yielding kinetic energy K_c = 1 2 I_c ^2 = 1 4 MR^2 ^2 . For the sphere about its diameter, I_s = 2 5 MR^2 , with kinetic energy K_s = 1 2 I_s( /2)^2 = 1 20 MR^2 ^2 . The ratio simplifies as follows: K_s K_c =