Question

Two solid cylinders P and Q of 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 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 translational kinetic energy
D. Cylinder `Q` reaches the ground with larger angular speed.

Answer 1

Correct Answer - D
`I_(P)gtI_(Q)`
`a_(P)=(gsintheta)/(1+(I_(P))/(mR^(2))), a_(Q)=(gsintheta)/(1+(I_(Q))/(mR^(2)))`
`a_(P)lta_(Q)impliesV=u+atimpliestprop1/a`
`t_(P)gtI_(Q)`
`V^(2)=u^(2)+2` as `impliesvpropaimpliesV_(P)ltV_(Q)`
Translation `KE, 1/2 mV^(2)implies"TR" KE_(P)lt"TR"K_(Q)`
`V=omegaRimpliesomegapropVimpliesomega_(P)ltomega_(Q)`