A uniform ball of radius `R` rolls without slipping between the rails such that the horizontal distance is `sqrt(3)R` between the two contact points of te rails of the ball. Figure (a) shows front view of the ball and figure (b) shows the side view of the ball. `v_(CM)` is the velocity of centre of mass of the ball and `omega` is the angular velocity of the ball after rolling down a distance `2h` along the incline then

Options

A. `V_(CM)=omegaR`
B. `V_(CM)=omega R/2`
C. `V_(CM)=sqrt((10gh)/13)`
D. `V_(CM)=sqrt((10 gh)/7)`

Answer

B, C

Explanation

`v_(CM)=omega sqrt(R^(2)-(3R^(2))/4)=omega R/2` (from pure rolling)
`mgh=1/2mv_(cm)^(2)+1/2 2/5 mR^(2)omega^(2)` (from conservation of energy)
`:.v_(CM)=sqrt((10gh)/13)`