A small object of uniform density rolls up a curved surface with an initial velocity

A small object of uniform density rolls up a curved surface with an initial velocity v’.It reaches upto a maximum height of 3v² / 4g with respect to the initial position.The object is

Options

(a) ring
(b) solid sphere
(c) hollow sphere
(d) disc

Correct Answer:

disc

Explanation:

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  • Conservation of mechanical energy:
    Initial total energy=Final total energy
    i.e. (K.E.+P.E.)1=(K.E.+P.E.)2
    1/2mv^2{1+K^2/R^2}+0=0+mgh
    1/2mv^2{1+K^2/R^2}=mg(3v^2/4g)
    1/2{1+K^2/R^2}=3/4
    1+K^2/R^2=3/2
    Hence,K^2/R^2=1/2
    which implies that the small object is disc

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