A sphere and a hollow cylinder roll without slipping down two separate inclined planes and travel the same direction in the same time. If the angle of the plane dowm which the sphere rolls is `30^(@)` , the angle of the other pane is

Options

A. `60^(@)`
B. `53^(@)`
C. `37^(@)`
D. `45^(@)`

Answer

D

Explanation

For rolling, `t=sqrt((2l(1+K^(2)//R^(2)))/(g sin theta))="same"`
(given in question)
`therefore" "(2l(1+K_(1)^(2)//R^(2)))/(g sin theta_(1))=(2l(1+K_(2)^(2)//R^(2)))/(g sin theta_(2))`
For sphere, `K_(1)^(2)=(2)/(5)R^(2), theta_(1)=30^(@)`
For hollow cylinder, `K_(2)^(2)=R^(2), theta_(2)=?`
`(1+(2)/(5))/(sin 30^(@))=(1+1)/(sin theta_(2)) or sin theta_(2)=(5)/(7)=0.7143`
`rArr" "theta_(2)=45^(@)`