Two bodies of same mass tied with an inelastic string of length `l` lie together. One of them is projected vertically upwards with velocity `sqrt(6gl)`. Find the maximum height up to which the centre of mass system of the two masses rises.

Answer

`l`

Explanation

Velocity of mass`-1` when string is in normal length.
`v_(A) = sqrt(6gl - 2gl) = 2 sqrtgl`
Now impulsive tension acts on both bodies to come to common velocity Desplacement of C.M. when string becomes taut.
`Deltay_(1 cm) = (m xx l + m xx 0)/(m + m) = (l)/(2)`
Desplacment of CM masses reach the max. height
`Deltay_(2 cm) = (v_(2))/(2g) = (l)/(2) :. Deltay_(cm) = (l)/(2) + (l)/(2) = l`