question_answer

A body starting from rest is moving at constant acceleration. After travelling a certain distance 10 m, its momentum is 50 N-s. What would be the momentum of the body after travelling 20 meters?

Answer:

Let the constant acceleration be a units. As the body is starting from rest, initial velocity of the body\[V=25\,m{{s}^{-1}}\]

Case-I	Case-II
\[{{m}_{A}}=1500\text{ }kg\]	then \[{{m}_{B}}=1000\text{ }kg\]
\[{{u}_{A}}=25\text{ }m/s\](given)	then \[{{u}_{B}}=15\text{ }m/s\]

\[P=m\times v\] .............(1) We know that, \[{{v}^{2}}-{{u}^{2}}=2aS\] \[\Rightarrow {{v}^{2}}-{{0}^{2}}=2aS\,\,\Rightarrow V=\sqrt{2aS}\]...........(2) Substituting (2) in (1), we get \[P=m\times v=m\times \sqrt{2aS}\Rightarrow P\propto \sqrt{S}\] (\[\because \] m and a are constant) \[\therefore \frac{{{P}_{1}}}{{{P}_{2}}}=\frac{\sqrt{10}}{\sqrt{20}}=\frac{1}{\sqrt{2}}\] \[\Rightarrow {{P}_{2}}=\sqrt{2}{{P}_{1}}=\sqrt{2}\times 50=50\sqrt{2}N-s\]