question_answer

A stationary tomb explodes into three pieces. One piece of 2 kg mass moves with a velocity of \[8\,m{{s}^{-1}}\] at right angles to the other piece of mass 1 kg moving with a velocity of \[12\,m{{s}^{-1}}\]. If the mass of the third piece of 0.5 kg, then its velocity is

A)  \[10\,m{{s}^{-1}}\]                        

B)         \[20\,m{{s}^{-1}}\]             

C)             \[30\,m{{s}^{-1}}\]                        

D)         \[40\,m{{s}^{-1}}\]

E)  \[50\,m{{s}^{-1}}\]

Correct Answer: D

Solution :

Momentum of third piece                 \[p=\sqrt{p_{x}^{2}+p_{y}^{2}}\]                 \[=\sqrt{{{(16)}^{2}}+{{(12)}^{2}}}\]                 \[=20\]                 \[v=\frac{p}{m}=\frac{20}{0.5}\] \[=40\text{ }m{{s}^{-1}}\]