Chapter 5, Problem 3RAT

Two iron, balls, one twice the mass of other, are dropped from rest from the top of a one- story building. Compared with lighter ball, the twice-as-heavy ball when hitting the ground below has

(a)half the momentum

(b)the same momentum

(c)twice the momentum

(d)four times the momentum

To determine

The correct option for the statement “Two iron balls, one twice the mass of other, are dropped from rest from the top of a one- story building. Compared with lighter ball, the twice-as-heavy ball when hitting the ground below has”.

Answer to Problem 3RAT

The correct option for the statement “Two iron balls, one twice the mass of other, are dropped from rest from the top of a one- story building. Compared with lighter ball, the twice-as-heavy ball when hitting the ground below has” is option (c).

Explanation of Solution

The momentum of an object changes due to change in either mass or speed of the object. It is necessary for change in the momentum that at least one quantity must vary.

Both balls are moving under the gravitational acceleration. The acceleration for both balls is same so the speed of both balls is also same.

The mass of one ball is two times the mass of the other ball, so the momentum of the heavier ball is two times the momentum of the lighter ball.

The momentum of the heavier ball becomes two times of the momentum of lighter ball only due to difference in the mass of both balls, not due to the speed of the balls.

Conclusion:

Therefore, the correct option (c) for the statement “Two iron balls, one twice the mass of other, are dropped from rest from the top of a one- story building. Compared with lighter ball, the twice-as-heavy ball when hitting the ground below has” is option (c).