An object of mass 100 kg falls from point A to B as shown in figure. The change in its weight corrected to the nearest integer is ( is the radius of the Earth) [2024]

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Solution

Q.
An object of mass 100 kg falls from point A to B as shown in figure. The change in its weight corrected to the nearest integer is ( $R_{E}$ is the radius of the Earth) [2024]

1 49 N

2 89 N

3 5 N

4 10 N

Ans.
(1)

Given, $m = 100 kg, g = 10 {m/s}^{2}$

$W_{A} = m g_{A} = m g {(\frac{R_{E}}{R_{E} + H_{B}})}^{2} = m g {(\frac{R_{E}}{R_{E} + 2 R_{E}})}^{2} = \frac{m g}{9}$

$W_{B} = m g_{B} = m g {(\frac{R_{E}}{R_{E} + H_{B}})}^{2} = m g {(\frac{R_{E}}{R_{E} + \frac{3 R_{E}}{2}})}^{2} = \frac{4 m g}{25}$

Change in weight $= W_{B} - W_{A}$

$= \frac{4 m g}{25} - \frac{m g}{9} = \frac{36 m g - 25 m g}{225}$

$= \frac{11 m g}{225} = \frac{11}{225} \times 100 \times 10 = 49$ $N$

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