A body hanging from a spring stretches it by 1 cm at the earth's surface. How much will the same body stretch the spring at a place 1600 km above the earth's surface? (ans in cm) (Radius of

Question

A body hanging from a spring stretches it by 1 cm at the earth's surface. How much will the same body stretch the spring at a place 1600 km above the earth's surface? (ans in cm) (Radius of earth = 6400 km )

TestHub · Accepted Answer

In equilibrium, weight of the body = stretching force
$∴$ At the earth's surface, ${mg}^{'} = k \times x^{'}$
$\Rightarrow \frac{g^{'}}{g} = \frac{x^{'}}{x} = \frac{R_{e}^{2}}{{(R_{e} + h)}^{2}}$
$= \frac{{(6400)}^{2}}{{(6400 + 1600)}^{2}} = \frac{16}{25}$
$\Rightarrow x^{'} = \frac{16}{25} \times x = \frac{16}{25} \times 1 cm = 0.64 cm$

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