Question

A ring of radius $R=4\text{m}$ has mass of $m_1=5.4$$\times {10}^9\text{kg}$, which is distributed uniformly over its circumference. A highly dense particle of mass $m_2=5.4$$\times {10}^9\text{kg}$ is placed along the axis of the ring at a distance $x_0=3\text{m}$ from the centre. Neglecting all other forces, except mutual gravitational interaction between the ring and particle. Calculate displacement of the ring when particle is at the centre of the ring.

• A. $1\text{m}$
• B. $1.5\text{m}$
• C. $2\text{m}$
• D. $3\text{m}$

Answer 1

The correct option is B $1.5\text{m}$

Let $x$ be the displacement of the ring. Then the displacement of the particle is $x_0-x$.

Since, there are no external forces, the center of mass of the system (ring+particle) will remain at rest. Hence,

$m_{1}x=m_2(x_0-x)$

$\Rightarrow x=\frac{m_2{x}_0}{m_1+m_2}$

Substituting the data given in the question,

$x=\frac{3\times 5.4\times {10}^9}{5.4\times {10}^9+5.4\times {10}^9}$

$\therefore x=1.5\text{m}$

Hence, option (b) is the correct answer.