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A small object of uniform density rolls ...

A small object of uniform density rolls up a curved surface with an initial velocity v. it reaches up to a maximum height of `(3v^2)/(4g)

with respect to the initial position. The object is

A

ring

B

solid

C

hollow sphere

D

disc

Text Solution

Verified by Experts

The correct Answer is:
D
(d) By the concept of energy conservation
`(1)/(2) mv^2 + (1)/(2)Iomega^2 = mg((3v^2)/(4g))`
`:. (1)/(2)mv^2 + (1)/(2)I(v^2)/(R^2) = (3)/(4)mv^2 [:. V = R omega]`
`:. (1)/(2)I (V^2)/(R^2) = (3)/(4)mv^2 - (1)/(2)mv^2 = (1)/(4)mv^2`
`rArr I = (1)/(2)mR^2`
This is the formula of the moment of inertia of the disc.
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