Question

Let G be the garvitational constant and R be the radius of earth. If the radius of the earth becomes half, the new value of gravitational constant will be

Answer 1

Answer:

G = 1.670 × $10^{-11}$ $m^{3}kg^{-1}s^{-2}$

Explanation:

From Newton's law of universal gravitation,

F = $\frac{GMm}{R^{2} }$

Where F is the force of attraction, G is the gravitational constant, M is the mass of the earth, R is the radius of the earth.

From Newton's second law of motion,

F = mg

mg = $\frac{GMm}{R^{2} }$

g = $\frac{GM}{R^{2} }$

⇒    G = $\frac{gR^{2} }{M}$

If the radius of the earth becomes half,

R = $\frac{R}{2}$, then;

G = $\frac{gR^{2} }{4M}$

Given that: g = 9.8 m/$s^{2}$, radius of the earth is 6371000 m, mass of the earth is 5.972 × $10^{24}$kg, then;

G   = $\frac{9.8*(6371000)^{2} }{4*5.972*10^{24} }$

   = 1.670 × $10^{-11}$ $m^{3}kg^{-1}s^{-2}$