If the acceleration due to gravity experienced by a point mass at a height h above the surface of earth is same as that of the acceleration due to gravity at a depth α h (h Re) from the earth surface. The value of α will be _________. (use Re = 6400 km) Numerical answer type. Work it out, then open the answer.

Answer: 2. Height h R: gh = g(1 - 2h/R) Depth α h: gd = g(1 - (α h)/(R)) Equal: α h = 2h ⇒ α = 2 So α = 2.

If the acceleration due to gravity experienced by a point mass at a… | JEE Main 2022 (29 Jul, Shift 1)

Q82JEE Main 2022 · 29 JUL · SHIFT 1Medium

Acceleration Due to Gravity

If the acceleration due to gravity experienced by a point mass at a height h above the surface of earth is same as that of the acceleration due to gravity at a depth $\alpha h\ (h \ll R_e)$ from the earth surface. The value of $\alpha$ will be _________.

(use $R_e = 6400\text{ km})$

Numerical answer type. Work it out, then open the answer.

Show answer and solution

Answer: 2

Height $h \ll R$ : $g_h = g\left(1 - \frac{2h}{R}\right)$
Depth $\alpha h$ : $g_d = g\left(1 - \frac{\alpha h}{R}\right)$
Equal: $\alpha h = 2h \Rightarrow \alpha = 2$
So $\alpha = 2$ .

Report a mistake

Acceleration Due to Gravity question from JEE Main 2022 (29 Jul, Shift 1)

More questions on Acceleration Due to Gravity