A small object of uniform density rolls up a curved surface with an initial velocity v . It reaches

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6.System of Particles and Rotational Motion

hard

A small object of uniform density rolls up a curved surface with an initial velocity $v$. It reaches up to a maximum height of $\frac{3 \mathrm{v}^2}{4 \mathrm{~g}}$ with respect to the initial position. The object is

A

ring

B

solid sphere

C

hollow sphere

D

disc

(IIT-2007)

Solution

$v =\sqrt{\frac{2 g h}{1+\frac{ k ^2}{ r ^2}}}$

$v ^2=\frac{2 g 3 v ^2}{4 g \left(1+\frac{ k ^2}{ r ^2}\right)}$

$\Rightarrow 1+\frac{ k ^2}{ r ^2}=\frac{3}{2}$

$k ^2=\frac{1}{2} r ^2 \rightarrow \text { disc }$

Standard 11

Physics

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