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Q.

A solid sphere of mass 1.5 kg rolls on a frictionless horizontal surface, its centre of mass moving at a speed of 5 $m s^{- 1}$ . Then it rolls up an incline of $30 °$ to horizontal. The height attained by the sphere before it stops is $(g = 10 m s^{- 2})$

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a

5 m

b

1.5 m

c

3.65 m

d

1.75 m

answer is C.

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Detailed Solution

The total mechanical energy is conserved.

$\frac{1}{2} m v^{2} (1 + \frac{k^{2}}{r^{2}}) = m g h$

$\Rightarrow \frac{5^{2}}{2} (1 + \frac{2}{5}) = 10 \times h \Rightarrow h = 1.75 m$

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