Question

The gravity of earth is measured at heights h, 2h and at depths h, 2h from the surface of the earth. The measurement of gravity is maximum [Given: h << radius of earth]

• A. At height h above the surface of earth
• B. At depth h below the surface of earth
• C. At depth 2h below the surface of earth
• D. Same at height h above the surface and depth h below the surface

Answer 1

The correct option is B At depth h below the surface of earth

Let R be the radius of the earth.

Value of acceleration due to gravity at height $h,g_h=g(1-\frac{2h}{R})$

Value of acceleration due to gravity at height $2h,g_{2h}=g(1-\frac{2\left(2h\right)}{R})=g(1-\frac{4h}{R})$

Value of acceleration due to gravity at depth $h,g_h^{\prime }=g(1-\frac{h}{R})$

Value of acceleration due to gravity at depth $2h,g_{2h}^{\prime }=g(1-\frac{2h}{R})$

From the above four equations, we can conclude that the value of g is maximum when it is measured at depth h from the surface of the earth.

Hence, the correct answer is option (b).