At the surface:
\[mg = 300 \, \text{N}\]
\[m = \frac{300}{g_s}\]
At depth \( \frac{R}{4} \):
\[g_d = g_s \left( 1 - \frac{d}{R} \right)\]
where \( d = \frac{R}{4} \).
\[g_d = g_s \left( 1 - \frac{R}{4R} \right) = g_s \cdot \frac{3}{4}\]
The weight at depth \( \frac{R}{4} \) is:
\[\text{Weight} = m \times g_d = m \times \frac{3 g_s}{4}\]
\[= \frac{3}{4} \times 300 = 225 \, \text{N}\]
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: The kinetic energy needed to project a body of mass $m$ from earth surface to infinity is $\frac{1}{2} \mathrm{mgR}$, where R is the radius of earth. Reason R: The maximum potential energy of a body is zero when it is projected to infinity from earth surface.
Match List-I with List-II: List-I