Question

A bullet $ ({{m}_{1}}=25\,g) $ fired with a velocity 400 m/s gets embedded into a bag of sand $ ({{m}_{2}}=4.9\,kg) $ suspended by a rope. The velocity gained by the bag is nearly:

• A. 2 m/s
• B. 4 m/s
• C. 8 m/s
• D. 0.2 m/s

Answer 1

Answer: (A)

Linear momentum of a system is conserved in absence of any external force. Conservation of linear momentum gives
$ {{m}_{1}}\,{{u}_{1}}+{{m}_{2}}\,{{u}_{2}}=({{m}_{1}}+{{m}_{2}})v $
Given, $ {{m}_{1}}=25g,\,{{u}_{1}}=400\,m/s $
$ {{m}_{2}}=4.9\,kg,\,\,{{u}_{2}}=0,\,v=.... $
Hence,
$ \frac{25}{1000}\times 400+4.9\times 0=\left( \frac{25}{1000}+4.9 \right)v $
or $ v=\frac{10000}{4925}\approx 2\,m/s $
Note: Since, bullet is embedded into bag, hence the collision is inelastic. But still the momentum is conserved.