A body is hanging from a rigid support. by an inextensible string of length `'1'` . It is struck inelastically by an identical body of mass in with horizontal velocity `v=sqrt(2gl)` the tension in the string increases just after the striking by

Options

A. `mg`
B. `3mg`
C. `2mg`
D. none of these

Answer

C

Explanation

Conservation of linear momentum of the system of bodies just before and after collision yields
`mv_(0)=(m+m)vimpliesv=v_(0)/2`
` :.` The tension in the string `T=((2m)v^(2))/l+(2m)g`
`T=(2mv_(0)^(2))/(4l)+2mg=(m(2gl))/(2l)+2mg=3mg`
initially the tension `=T_(0)=mg`
`implies` increase `n` tension `=2mg`