Two pendulums each of lengh l are initially situated as shown in figure. The first pendulum is released and strikes the second. Assume that the collision is completely inelastic and neglect the mass of the string and frictional effects. How high does the centre of mass rise after the collision ?

Options

A. `d[(m_(1))/((m_(1)+m_(2)))]^(2)`
B. `d[(m_(1))/((m_(1)+m_(2)))]`
C. `(d(m_(1)+m_(2))^(2))/m_(2)`
D. `d[(m_(2))/((m_(1)+m_(2)))]^(2)`

Answer

A

Explanation

By conservation of momentum
`m_(1)v_(1)=(m_(1)+M_(2))V`
`or m_(1)sqrt(2gd)=(m_(1)+m_(2))v`
let centre of mass rise through a height h
`1/2(m_(1)+m_(2))v^(2)=(m_(1)+m_(2))gh`
`h=d{(m_(1))/(m_(1)+m_(2))}^(2)`