A small object of uniform density rolls up a curved surface with an initial velocity v^ . It reaches up to a maximum height of (3 v^2)/(4 g) with respect to the initial position. The object is

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Correct answer: D. disc

As v= (2 g h)/(1+(k^2)/(r^2)) Given h=(3 v^2)/(4 g) v^2=(2 g h)/(1+(k^2)/(r^2))=(2 g 3 v^2)/(4 g(1+(k^2)/(r^2)))=(6 g v^2)/(4 g(1+(u^2)/(v^2))) 1=(3)/(2(1+(k^2)/(v^2))) or 1+(k^2)/(r^2)=(3)/(2) or (k^2)/(r^2)=(3)/(2)-1=(1)/(2) k^2=(1)/(2) r^2 (Equation of disc) Hence, the object is disc.

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