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

G = 1.670 ×

Explanation:

From Newton's law of universal gravitation,

F =

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 =

g =

⇒    G =

If the radius of the earth becomes half,

R = , then;

G =

Given that: g = 9.8 m/, radius of the earth is 6371000 m, mass of the earth is 5.972 × kg, then;

G   =

   = 1.670 ×

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