Question

Three particles X, Y, and Z of masses 2 kg, 5 kg, and 4 kg respectively are arranged in order along a straight line. Y is 5.0 m from X and 7.0 m from Z. The distance of the centre of mass of the system of mass from X is?

ANS: 6.6 m

Help please? I don't even know how to start :(

Answer 1

The C.M of the system is closer to the heavier mass 5kg. Assume the C.M is a distance d from Y. mass 2kg is (5+d)m from c.m of system.5kg is dm from c.m and 4kg is (7-d)m from c.m taking moment about c.m:2(5+d)+5d=4(7-d) 10+2d+5d=28-4d 11d=18 d=1.64m c.m is (5+1.64)m=6.64m from X(approx is 6.6m)