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

Options

A. Ring
B. Solid sphere
C. Hollow sphere
D. Disc

Answer

D

Explanation

(d) From law of conservation of mechanical energy
`Delta K + Delta U = 0`
`[0 -((1)/(2) I omega^2 + (1)/(2) mv^2)] + (mg xx (3 v^2)/(4 g)) = 0`
`rArr (1)/(2) I omega^2 = (3)/(4) mv^2 - (1)/(2) mv^2 = (mv^2)/(2) ((3)/(2) - 1)`
As cylinder is rolling `omega = (v)/( R)`
or `(1)/(2) I (v^2)/(R^2) = (mv^2)/(4)` or `I = (1)/(2) mR^2`
Hence, object is a disc.
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