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Gravitational force of attraction

A ring of radius R=4 {~m} is made of a highly dense material.

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Solving time: 3 mins

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

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Book:

Mechanics Volume 2 (DC Pandey)

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Charlotte Discussed

A ring of radius

R = 4 m

is made of a highly dense material. Mass of the ring is

m_{1} = 5.4 \times 1 0^{9} kg

distributed uniformly over its circumference. A highly dense particle of mass

m_{2} = 6 \times 1 0^{8} kg

is placed on the axis of the ring at a distance

x_{0} = 3 m

from the centre. Neglecting all other forces, except mutual gravitational interaction of the two. Calculate (i) displacement of the ring when particle is at the centre of ring, and (ii) speed of the particle at that instant.

8 mins ago

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Text solutionVerified

(a) Let

x

be the displacement of ring. Then displacement of the particle is

x_{0} - x

, or

(3.0 - x) m

. Centre of mass will not move. Hence,

(5.4 \times 1 0^{9}) x = (6 \times 1 0^{8}) (3 - x)

Solving, we get

x = 0.3 m

(b) Apply conservation of linear momentum and conservation of mechanical energy.

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Question Text	A ring of radius $R = 4 m$ is made of a highly dense material. Mass of the ring is $m_{1} = 5.4 \times 1 0^{9} kg$ distributed uniformly over its circumference. A highly dense particle of mass $m_{2} = 6 \times 1 0^{8} kg$ is placed on the axis of the ring at a distance $x_{0} = 3 m$ from the centre. Neglecting all other forces, except mutual gravitational interaction of the two. Calculate (i) displacement of the ring when particle is at the centre of ring, and (ii) speed of the particle at that instant.
Topic	Gravitation
Subject	Physics
Class	Class 11
Answer Type	Text solution:1
Upvotes	117

Text solutionVerified

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