UPSEE Solved Model Paper 3

Here, the x - coordinate of centre of mass of the system remainds unchanged when the mass m moved a distance L cos θ.
Let the mass (m + M) moves a distance x in the backward direction, (from the theory of centre of mass, chnage in coordinate of centre of mass = 0)
∴ (M + m) x - mL cos θ = 0
∴ x =

mLcosθ

m+M