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 given by ______.

Options

• `"2u"/(1+"m"/"M")`

• `"2u"/(1+"M"/"m")`

• `(2"uM")/"m"`

• `"2um"/"M"`

Answer 1

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 given by `underline("2u"/(1+"m"/"M"))`.

Explanation:

Velocity of the second sphere is given by

`"V"_2=(2"m"_1"u"_1)/("m"_1+"m"_2)+("m"_2-"m"_1)/("m"_1+"m"_2)*"u"_2`

Here m1 = M, m₂ = m, u₁ = u, v₂ = v, u₂ = 0

`therefore"v"=(2"Mu")/("M"+"m")="2u"/(1+"m"/"M")`