A ball of mass $m$ travelling with velocity $5 v$ collides with and sticks to a ball of mass $5 m$ travelling in the same direction with velocity $v$ .Their common velocity after the collision is

$v$

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$\frac{6 v}{5}$

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$\frac{8 v}{10}$

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$\frac{5 v}{3}$

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Solution

The correct option is D
$\frac{5 v}{3}$

Step 1: Given data
Mass of ball is $m_{1} = m$
Velocity of ball is $v_{1} = 5 v$
Mass of another ball is $m_{2} = 5 m$
Velocity of another ball is $v_{2} = v$ .
Step 2: Finding the velocity of combined mass
After collision, the two masses stick together and consider its velocity will be $V .$
Applying Conservation of momentum,
$m_{1} \times v_{1} + m_{2} \times v_{2} = m \times V m \times 5 v + 5 m \times v = 6 m \times V 5 m v + 5 m v = 6 m V 10 m v = 6 m V V = \frac{10 m v}{6 m} V = \frac{5 v}{3}$
Thus, the common velocity after the collision is $\frac{5 v}{3} .$
Hence, option (d) is correct.

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