question_answer

A block of mass m=10 kg rests on a horizontal table. The coefficient of friction between the block and the table is 0.05. When hit by a bullet of nails 50 g moving with speed r, that gets embedded in it, the block moves and comes to stop after moving a distance of 2 m on the table. If a freely falling object were to acquire speed \[\frac{\upsilon }{10}\] after being dropped from height H, then neglecting energy losses and taking \[g=10m{{s}^{-2}},\]the value of H is close to: JEE Main Online Paper (Held On 10 April 2015)

A)  0.2 km

B)  0.4 km

C)  0.5 km

D)  0.3 km

E)  None of the above

Correct Answer: E

Solution :

                (*) If block to come to rest after 2m. So, \[d=\frac{{{u}^{2}}}{2a}\] \[a=\mu g=0.05\times 10=0.5m/{{\sec }^{2}}\] \[{{u}^{2}}=2\times 2\times 0.5=2\] \[u=\sqrt{2}m/\sec \]by momentum conservation \[\sqrt{2}\left( 10+50\times {{10}^{-3}} \right)=\left( 50\times {{10}^{-3}} \right)\times V\] approximately \[\frac{\sqrt{2}\times 10}{50\times {{10}^{-3}}}=V\] \[V=200\sqrt{2}m/\sec \]so \[\frac{V}{10}=20\sqrt{2}\] to get \[V=20\sqrt{2}m/\sec \]  \[{{V}^{2}}=2gh\] \[h=\frac{800}{20}=40m\]