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When a solid sphere rolls without slippi...

When a solid sphere rolls without slipping down an inclined plane making an angle `theta` with the horizontal, the acceleration of its centre of mass is `a`. If the same sphere slides without friction, its acceleration is:

A

`7/2` a

B

`5/7` a

C

`7/5` a

D

`5/2` a

Text Solution

Verified by Experts

The correct Answer is:
C
Acceleration of the solid sphere when it rolls without slipping down an inclined plane is
`a=(gsintheta)/(1+ I/(MR^(2))`
For a solid sphere, `I=1/5MR^(2)`
`therefore a=(gsintheta)/(1+2/5) = 5/7g sintheta`…………..(i)
Accleration of the same sphere when it slides without friction down an same inclined plane is
`a^(') = gsintheta` ............(ii)
Dividide (ii) by (i), we get
`a^(')/(a) = 7/5`or `a^(')=7/5a`
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