Question

Two masses M1 and M2 placed at a distance 'I' part,let the centre of mass of this system be at a point named C. If M1 is displaced by L1 towards C and M2 is displaced by L2 away from C, find the distance from C where the new centre of mass will be located.

Answer 1

Initially the centre of mass is at C,
let x be the distance for m1 and L-x distance for m2 from centre of mass C.
m1x = m2(L-x)...........(1)
After getting displaced the eqn. would form,
m1(L1 + x – h) = m2(L – x + h + L2)...........(2)
solving eqns. (1) and (2) we get,
m1L1 +m1x – m1h = m2L - m2x + m2L2 + m2h
h(m1 + m2) = (m1 + m2)x + m1L1 – m2L – m2L2
h = (m1L1 – m2L)/(m1 +m2)