NEET Physics Mathematical Tools, Units & Dimensions NEET PYQ-Mathematical Tools, Units and Dimensions

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 [AIPMT (M) 2012]

A) 68%

B) 41%

C) 200%

D) 100%

Correct Answer: B

Solution :

Velocity \[v=\sqrt{2gh}\] ... (i)

and momentum\[p=\text{ }mv\] ... (ii)

From Eqs. (i) and (ii), we have

\[p\propto \sqrt{h}\]

Here \[\frac{{{p}_{2}}}{{{p}_{1}}}=\sqrt{\frac{{{h}_{2}}}{{{h}_{1}}}}\]

\[\therefore \] \[\frac{{{p}_{2}}}{{{p}_{1}}}=\sqrt{\frac{2h}{h}}=\sqrt{2}\]

\[{{p}_{2}}=1.414{{p}_{1}}\]

% change \[=\frac{{{p}_{2}}-{{p}_{1}}}{{{p}_{1}}}\times 100=41%\]