A smooth sphere of mass 𝑀 moving with velocity 𝑢 directly collides elastically with another sphere of
mass 𝑚 at rest. After collision their final velocities are 𝑉 and 𝑣 respectively. The value of 𝑣 is

Question: A smooth sphere of mass 𝑀 moving with velocity 𝑢 directly collides elastically with another sphere of mass 𝑚 at rest. After collision their final velocities are 𝑉 and 𝑣 respectively. The value of 𝑣 is

(A) \dfrac{2uM}{m}

(B) \dfrac{2um}{M}

(C) \dfrac{2u}{1+\dfrac{m}{M}}

(D) \dfrac{2u}{1+\dfrac{M}{m}}

Answer: Option (C)

Solution:

A smooth sphere of mass 𝑀 moving with velocity 𝑢 directly collides elastically with another sphere of
mass 𝑚 at rest. After collision their final velocities are 𝑉 and 𝑣 respectively. The value of 𝑣 is
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