Discussion Forum



1)

Two solid cylinders P and Q of the same mass and same radius start rolling down a fixed inclined plane from the same height at the same time. Cylinder P has most of its mass concentrated near its surface, while Q has most of its mass concentrated near the axis. Which statement(s) is(are) correct?


A) Both cylinders P and Q reach the ground at the same time

B) Cylinder P has larger linear acceleration than cylinder Q

C) Both cylinders reach the ground with same transiational kinetic energy

D) Cylinder Q reaches the ground with larger angular speed

Answer:

Option D

Explanation:

$I_{P} >I_{Q}$

 In case of pure rolling,

   $a=\frac{g \sin \theta}{1+I/mR^{2}}$

$a_{Q} >a_{p}$  as its moment of inertia is less.

Therefore, Q reaches first with more linear speed and more translational kinetic energy.

 Further, $\omega=\frac{v}{R}$

 or   $\omega \propto V$

$\therefore$   $\omega_{Q} >\omega_{P}$                as   $v_{p} >v_{Q}$