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A thin metal disc of mass 2 kg starts fr...

A thin metal disc of mass 2 kg starts from rest and rolls down a smooth inclined plane. Its rotational K.E. is 4 J at the bottom of the inclined plane. What is its linear velocity at the same point?

A

`3sqrt2m//s`

B

`2sqrt3m//s`

C

`2sqrt2 m//s`

D

`2m//s`

Text Solution

Verified by Experts

The correct Answer is:
C
Rotational K.E. `=(1)/(2)Iomega^(2)" for a disc, I"=(1)/(2)mr^(2)`
`=(1)/(2).((1)/(2)mr^(2))(v^(2))/(r^(2))=(1)/(4)mv^(2)`
But it is given than Rotational K.E. = 4J
`therefore" "4=(1)/(4)xx2xxv^(2)" "therefore v^(2)=8" "therefore v=2sqrt2 m//s`
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