Question

Two skaters A and B of masses 50 kg and 70 kg respectively stand facing each other 6 m apart. Then they pull on a rope stretched between them. How far has each moved when they meet?

• A. Both 3 m
• B. A moves 2.5 and B, 3.5 m
• C. A moves 3.5 and B, 2.5 m
• D. A moves 2m and B, 4 m

Answer 1

Answer: (C)

A moves 3.5 and B, 2.5 m

Point $O$ represents the centre of mass of the system.

Using $x=\frac{M_A\left(OA\right)+M_B\left(AB\right)}{M_{total}}$

$x=\frac{50\times \left(0\right)+70\left(6\right)}{50+70}=3.5$ m

$⟹$ $y=6-3.5=2.5$ m

Pulling the rope does not involve any external force, thus their $COM$ remains at rest i.e they meet at their centre of mass.

$⟹$ A moves 3.5 m and B moves 2.5 m