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A particle of mass m, moving with veloci...

A particle of mass `m`, moving with velocity `v` collides a stationary particle of mass `2m`. As a result of collision, the particle of mass `m` deviates by `45^@` and has final speed of `v/2`. For this situation mark out the correct statement (s).

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The correct Answer is:
B, D
Momentum remains conserved in any type of equation

`p_i=p_f`
`:. (mvhati)=((mv)/(2sqrt2)hati+(mv)/(2sqrt2)hatj)+(2m)v`

v=velocity of mass `2m`
`=0.32hati-0.35hatj`
`=(0.32v)hati-(0.18v)hatj`
`V=0.37v`
`tan theta=(0.18v)/(0.32v)=0.5625`
`:. theta=29.35^@`
Since `(theta+45^@)lt90^@`. Therefore, the angle of divergence between particles after collision is less than `90^@`.
Further, `K_i=1/2mv^2` and
`K_f=1/2m(v/2)^2+1/2(2m)(0.37v)^2`
`K_(f)ltK_(i)`
Therefore, collision is inelastic.
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