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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