Two bodies of the same mass are connected with an inelastic string of length 1 are placed together on a horizontal surface. One of them is projected vertically upwards from the surface with a velocity `u=sqrt(6gl)`. The maximum height up to which the centre of mass of the system of two masses rises is

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`