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A solid sphere and a solid cylinder havi...

A solid sphere and a solid cylinder having the same mass and radius, roil down the same incline. The ratio of their acceleration will be

A

`15:14`

B

`sqrt(15) : sqrt(14)`

C

`14 : 15`

D

`sqrt(14) : sqrt(15)`

Text Solution

Verified by Experts

The correct Answer is:
D
In case of pure rolling, `a=(g sin theta)/(1+(I)/(mR^(2)))`
`(I)/(mR^(2))=(2)/(5)` for sphere and `(I)/(MR^(2))=(1)/(2)` for a disc
`:.` For a solid sphere, `a_(1)=(5)/(7)g sin theta`
and for a hollow sphere, `a_(2)=(2)/(3)g sin theta`
From `s=(1)/(2)at^(2),t=sqrt((2s)/(a))or (t_(1))/(t_(2))=sqrt((a_(2))/(a_(1)))=sqrt((2//3)/(5//7))=sqrt((14)/(15))`.
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