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  4. If a man weighs 90 kg on the surface of the earth, the height above the surface of the earth of radius R, where the weight is 30 kg is

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Q. If a man weighs $90 \, kg$ on the surface of the earth, the height above the surface of the earth of radius $R,$ where the weight is $30 \, kg$ is

NTA AbhyasNTA Abhyas 2022

Solution:

Given, $\frac{m g ′}{m g}=\frac{30}{90}$ or $\frac{g ′}{g}=\frac{1}{3}$
Now, $g^{′}=g\frac{R^{2}}{\left(R + h\right)^{2}}$ or $\frac{g ′}{g}=\frac{R^{2}}{\left(R + h\right)^{2}}=\frac{1}{3}$
or $\frac{R}{R + h}=\frac{1}{\sqrt{3}}$ or $\left(R + h\right)=\sqrt{3}R$
or $h=\left(\sqrt{3} - 1\right)R=0.73R$