# A spherical ball of mass 20 kg is stationary at the top of a hill of height 100 m . It rolls down a smooth surface to the ground, then climbs up another hill of height 30 m and finally rolls down to a horizontal base at a height of 20 m above the ground. The velocity attained by the ball is Option 1) 10 m/s Option 2) 34 m/s Option 3) 40 m/s Option 4) 20 m/s

As we learnt in

If only conservative forces act on a system, total mechnical energy remains constant -

$K+U=E\left ( constant \right )$

$\Delta K+\Delta U=0$

$\Delta K=-\Delta U$

-

Since surface is smooth so the motion of ball is not rolling motion change in kinetic energy = loss in potential energy

$\Rightarrow\ \frac{1}{2}mv^{2}=mg(h_{i}-h_{f})$

$v=\sqrt{}{2g(h_{i}-h_{f})}=\sqrt{}{2\times 10\times 80}$

v = 40 m/s

Option 1)

10 m/s

This is an incorrect option.

Option 2)

34 m/s

This is the correct option.

Option 3)

40 m/s

This is an incorrect option.

Option 4)

20 m/s

This is an incorrect option.

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