Question

A ball of mass m is thrown vertically upward from the ground and reaches a height h before momentarily coming to rest.If g is acceleration due to gravity,the impulse received by the ball due to gravity force during its flight is

• A. $\sqrt{2m^{2}gh}$
• B. $\sqrt{4m^{2}gh}$
• C. $\sqrt{8m^{2}gh}$
• D. $4\sqrt{m^{2}gh}$

Answer 1

The correct option is A $\sqrt{2m^{2}gh}$

Since the ball is under force of gravity it is moving with acceleration.

$v^2-u^2=-2gh$

$u=\sqrt{2gh}$

$v=u+at$

$0=\sqrt{2gh}-gt$

$t=\frac{\sqrt{2gh}}{g}=\sqrt{\frac{2h}{g}}$

Impulse $={\int }_0^{t}Fdt$

Since F is constant,

Impulse $=F{\int }_0^{t}dt=Ft$

$=mg\times \sqrt{\frac{2h}{g}}=\sqrt{2m^{2}gh}$