A steel sphere is dropped vertically onto a horizontal metal plate.

Question 25

A steel sphere is dropped vertically onto a horizontal metal plate. The sphere hits the plate with speed u, leaves it at speed v, and rebounds vertically to half of its original height. Ignore air resistance.

Which expression gives the value of v / u ?

A 1 / 2²                        B 1 / 2                         C 1 / √2                       D 1 – 1/√2

Reference: Past Exam Paper – June 2018 Paper 12 Q18

Solution:

Answer: C.

Let the height from which the sphere is dropped = h.

As the sphere falls, its gravitational potential energy gets converted into kinetic energy. Its speed when it hits the plate is u.

mgh = ½ mu²

Speed u = √(2gh)

As the sphere rebounds and move vertically up, its kinetic energy gets converted into gravitational potential energy. The height is now half the height where it has dropped initially.

½ mv2 = mg(h/2)

Speed v = √(gh)

Ratio = v / u = √(gh) / √(2gh)

Ratio = v / u = √(gh) / [√(gh) × √2]

Ratio = v / u = 1 / √2