Question

A stone is dropped from a height $h$. It hits the ground with a certain momentum $P$. If the same stone is dropped from a height $100$% more than the previous height, the momentum when it hits the ground will change by (approximately) :

• A. $41$%
• B. $53$%
• C. $60$%
• D. $68$%

Answer 1

The correct option is A $41$%

Velocity, $v=\sqrt{2gh}$

Momentum, $P=mv=m\sqrt{2gh}$

$P\propto \sqrt{h}$

$\frac{P_2}{P_1}=\sqrt{\frac{h_2}{h_1}}=\sqrt{\frac{2h}{h}}=\sqrt{2}$

$P_2=1.414P_1$

% change $=\frac{P_2-P_1}{P_1}\times 100$%

$\frac{1.414P_1-P_1}{P_1}\times 100$

% change $=41.4$%