Question

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 and then climbs up another hill of height 30 m and finally rolls down to a horizontal base at a height 20 m above the ground. The velocity attained by the ball is:

• A. 40 ms${}^{-1}$
• B. 20 ms${}^{-1}$
• C. 10 ms${}^{-1}$
• D. 10 $\sqrt{30}$ ms${}^{-1}$

Answer 1

Answer: (A)

40 ms${}^{-1}$

For the potential energy, only the difference between the initial and final points count.

So this difference is $100-20=80m$

Conservation of energy

$\frac{1}{2}m{v}^2=mgh$

$0.5v^2=10\times 80$

$\Rightarrow v=40m/s$

Option A.