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 -

• A. 41 %
• B. 200 %
• C. 1
• D. 0.6

Answer 1

Answer: (A)

41 %

Answer 2

The correct answer is A:$41\%$
$v = \sqrt{2gh}$ (here,'v' is velocity)
$P = mv =m \sqrt{2gh}$ (here,'P' is momentum)
$P \propto\sqrt{h}$ (which states that P is directly proportional to $\sqrt{h}$)
$\frac{P_{2}}{P_{1}} = \sqrt{\frac{h_{2}}{h_{1}}} = \sqrt{\frac{2h}{h}} = \sqrt{2}$
$P_{2} = 1.414 P_{1}$
$\%$ change = $\frac{P_{2 } -P_{1}}{P_{1}} \times100\%$
$= 41.4 \%$