Question

Two unequal masses possess the same K.E. Then, the heavier mass has :

• A. greater momentum
• B. smaller momentum
• C. the lighter mass
• D. greater speed

Answer 1

The correct option is A greater momentum

Kinetic energy of two bodies are equal i.e

$\frac{1}{2}$m1v1${}^2$ = $\frac{1}{2}$m2v2${}^2$

$\frac{v{2}^2}{v{1}^2}$ = $\frac{m1}{m2}$

$\frac{v2}{v1}$ = $\sqrt{\frac{m1}{m2}}$

Linear momentum is given by,

p1 = m1v1 and p2 = m2v2

Therefore $\frac{p2}{p1}$ = $\frac{m2v2}{m1v1}$ = $\frac{m2}{m1}$ $\ast$ $\sqrt{\frac{m1}{m2}}$ = $\sqrt{\frac{m1m^2}{m2m{1}^2}}$

$\frac{p2}{p1}$ = $\sqrt{\frac{m2}{m1}}$

Thus mass has a direct dependence on linear momentum

Hence the heavier body will have a greater momentum