Question

Two man 'A' and 'B' are standing on opposite edge of a 6m long platform which is further kept on a smooth floor. They starts moving towards each other and finally meet at the midpoint of platform. Find the displacement of platform. Find the displacement of platform if mass of A, B and platform are 40 kg, 60 kg and 50 kg respectively.

Answer 1

In this no external force is acting as a center of mass will not move

initially as shown in the diagram position center of mass is constant

$d_{cm}=\frac{50\times 3+60\times 6}{40+50+60}$ .....eq1

After interchanging the position of A and B the plank displace x distance

$d_{cm}=\frac{60\times x+50\times (3+x)+40\times (6+x)}{40+50+60}$... ..eq2

from eq1 and eq2 we get

$\frac{50\times 3+60\times 6}{40+50+60}=\frac{60\times x+50\times (3+x)+40\times (6+x)}{40+50+60}$

$\Rightarrow 150x=120$

$\Rightarrow x=\frac{4}{5}=0.8m$