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A body of mass ‘m’ moving with a velocity 8m/s collide with another body of mass 15kg moving with 4m/s in opposite direction, after collision they stick and move together, then the loss of K.E is 270J. Then m is ____

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20 kg

5 kg

10 kg

15 kg

answer is A.

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Detailed Solution

Let the masses and velocities be $m_{1}, m_{2} and v_{1}, v_{2}$

The final velocity of the combined mass will be $\frac{m_{1} v_{1} - m_{2} v_{2}}{m_{1} + m_{2}}$

$∆ K . E = \frac{1}{2} m_{1} {u_{1}}^{2} + \frac{1}{2} m_{2} {u_{2}}^{2} - \frac{1}{2} (m_{1} + m_{2}) {(\frac{m_{1} u_{1} - m_{2} u_{2}}{m_{1} + m_{2}})}^{2}$

$Δ K . E = \frac{1}{2} \frac{m_{1} m_{2}}{m_{1} + m_{2}} {(u_{1} + u_{2})}^{2}$

$270 = \frac{1}{2} \cdot (\frac{15 m}{m + 15}) (8 + 4)^{2} \Rightarrow m = 5 kg$

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