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  4. The weight of a body at earth's surface is W . At a depth halfway to the centre of the earth, it will be (assuming uniform density in the earth) -

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Q. The weight of a body at earth's surface is $W$ . At a depth halfway to the centre of the earth, it will be (assuming uniform density in the earth) -

NTA AbhyasNTA Abhyas 2022

Solution:

Due to depth $g^{′}=g \, \left\{1 - \frac{d}{R_{e}}\right\}\therefore \, d=R_{e} / 2$
so $g^{′}=g \, \left\{1 - \frac{R_{e} / 2}{R_{e}}\right\}=g / 2$
Now $g^{′}$ is half so weight is also half.