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A ring of radius $R = 4 m$ is made of a highly dense material. Mass of the ring is $m_{1} = 5.4 \times 10^{9} k g$ distributed uniformly over its circumference. A highly dense particle of mass $m_{2} = 6 \times 10^{8} k g$ is placed on the axis of the ring at a distance $x_{0} = 3 m$ from the center. Neglecting all other forces, except mutual gravitational interaction of the two. Calculate displacement of the ring when particle is at the center of ring.

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$0.2 m$

$0.4 m$

$0.3 m$

$0.1 m$

answer is C.

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Detailed Solution

Let $x$ be the displacement of ring. Then displacement of the particle is $x_{0} - x$ , or $(3.0 - x) m$ Center of mass will not move. Hence,

$(5.4 \times 10^{9}) x = (6 \times 10^{8}) (3 - x)$

Solving, we get $x = 0.3 m$ Ans.

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