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A mass sliding down an inclined plane an...

A mass sliding down an inclined plane and reaches the bottom with velocity v. If the same mass is in the form of a disc and rolls down the same inclined plane, what is its velocity at the bottom ?

A

v

B

`sqrt((2)/(3)v)`

C

`sqrt(2)v`

D

`(v)/(sqrt(2))`

Text Solution

Verified by Experts

The correct Answer is:
B
Here K.E. of mass = `(1)/(2)mv^(2)`
Total K.E. of disc = `(1)/(2)mv_(d)^(2)+(1)/(2)((1)/(2)mr^(2))omega^(2)`
`=(3)/(4)mv_(d)^(2)`
`therefore (3)/(4)mv_(d)^(2)=(1)/(2)mv^(2)`
or `v_(d)=sqrt((2)/(3))v`
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