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Centripetal Force

A mass m is s...

Question

A mass m is suspended form a sensitive spring balance kept in a satellite. The reading of the balance is $W_{1}$ when the satellite is in an orbit of radius R and is $W_{2}$ when it is in an orbit of radius 2R. Then,

W_{1} > W_{2}

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W_{1} < W_{2}

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W_{1} = W_{2}

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cannot be predicted

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Solution

The correct option is C $W_{1} = W_{2}$
For a body revolving around the earth at any orbital radius, the gravitational force towards earth is countered by centrifugal force as shown in figure.
i.e. $F_{g} = F_{v}$
So, for a body hanging in the satellite, $W_{1} + F_{v} = F_{g} \to W_{1} = 0$
Similarly, $W_{2} = 0$ . Thus $W_{1} = W_{2}$ .

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