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>> $A particle of mass m0, travelling at spe$

Question

A particle of mass $m_{0},$ travelling at speed $v_{0},$ strikes a stationary particle of mass $2 m_{0} .$ As a result, the particle of mass $m_{0}$ is deflected through $4 5^{o}$ and has a final speed of $\frac{v _{0}}{2}$ . Then the speed of the particle of mass $2 m_{0}$ after this collision is

A

$\frac{v _{0}}{2}$

B

$\frac{v _{0}}{2 2}$

C

$2 v_{0}$

D

$\frac{v _{0}}{2}$

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Updated on : 2022-09-05

Solution

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Correct option is B)

A particle of mass $m_{0},$
Before collision

$m v_{0} = 2 m v c o s θ + \frac{m v _{0}}{2} . . . . . . . . . . (i)$

$θ = \frac{m v _{0}}{2} - 2 m v s i n θ . . . . . . . . . . . . (i i)$

By (i) & (ii), $θ = 4 5^{0}$
Now again momentum conservation in y direction

$\frac{m v _{0}}{2} = 2 m v . \frac{1}{2} \Rightarrow v = \frac{v _{0}}{2 2}$

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