Question

A sphere X of mass $2\text{kg}$ is moving to the right at $10{\text{ms}}^{-1}$. Sphere Y of mass $4\text{kg}$is moving to the left at $10{\text{ms}}^{-1}$.The two spheres collide head-on. The ratio of the magnitude of the impulse exerted by X on Y to that exerted by Y on X is

• A. $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$
• B. $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$
• C. $1$
• D. $\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$1$}\right.$

Answer 1

The correct option is C

$1$

Step 1: Given data

Mass of sphere X $=2\text{kg}$

The velocity of sphere X $=10{\text{ms}}^{-1}\hat{\text{i}}$ ( as it is moving towards the right in the positive X direction)

Mass of sphere Y$=4\text{kg}$

The velocity of sphere Y $=10{\text{ms}}^{-1}\text{(-}\hat{\text{i}}\text{)}$ ( as it is moving toward the left in the negative X direction)

Step 2: Concept of Impulse

During the collision, an object experience an impulse and hence a change in momentum.

By, the impulse-momentum theorem, impulse = change in momentum.

The impulse experienced by an object will be equal to the change in velocity of the object if the mass is inconsiderate.

The magnitude of impulse exerted by X on Y = Magnitude of impulse exerted by Y on X, as the change in velocity will be the same in both cases.

Therefore, the ratio of impulse exerted by X on Y to that exerted by Y on X is 1

Hence, option C is correct.