JEE Physics 2023 Question with Solution

Step-by-step solution

Common mistakes

• Using the inverse square law for depth inside the earth is incorrect because that relation applies outside the earth. Inside a uniformly dense earth, weight decreases linearly with depth. Use $W' = W\left(1 - \frac{d}{R}\right)$ instead.

• Substituting $d = \frac{R}{2}$ incorrectly as $\frac{d}{R} = \frac{R}{2}$ is wrong because $\frac{d}{R} = \frac{R/2}{R} = \frac{1}{2}$. Always simplify the ratio carefully.

• Marking zero weight is incorrect because weight becomes zero only at the center of the earth, where $d = R$. Here the body is only at half the radius depth, so the weight is reduced but not zero.