KVPY2014PhysicsRotational Motion
A solid cylinder P rolls without slipping from rest down an inclined plane attaining a speed v_ p at the bottom. Another smooth solid cyclinder Q of same mass and dimensions slides without friction from rest down the inclined plane attaining a speed v_ q at the bottom. The ratio of the speeds ( v_ p v_ q ) is :
Options
- A( 3 4 )
- B( 3 2 )
- C( 2 3 )
- D( 4 3 )
Correct answer
C. ( 2 3 )
Step-by-step solution
m g h= 1 2 m v²+ 1 2 I ²m g h= 1 2 m v²+ 1 2 M R² ² 2 g h= 1 2 m v²+ 1 4 m v²= 3 4 v² array l V²= 4 g h 3 & V= 4 g h 3 V= 2 g h & V_ R = 4 3 2 = 2 / 3 array