question_answer

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

A) 40m/s              

B) 20 m/s

C) 10 m/s             

D) \[10\sqrt{30}\,m/s\]

Correct Answer: A

Solution :

According to conservation of energy, or \[mgH=\frac{1}{2}m{{\nu }^{2}}+mg{{h}_{2}}\] or \[mg(H-{{h}_{2}})\,\,=\,\,\frac{1}{2}m{{\nu }^{2}}\] \[\nu \,\,=\,\,\sqrt{2g\,(100-20)}\] or \[\nu \,\,=\,\,\sqrt{2\times 10\times 80}\,\,=\,\,40m/s\]