1.

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 ?

Answer»

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

Solution :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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