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

The Correct Option is A

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 = \(\frac{P_{2 } -P_{1}}{P_{1}} \times100\%\)
\(= 41.4 \%\)