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

G = 1.670 ×
`10^(-11)`
`m^(3)kg^(-1)s^(-2)`

Step-by-step explanation:

From Newton's law of universal gravitation,

F =
`(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 =
`(GMm)/(R^(2) )`

g =
`(GM)/(R^(2) )`

⇒ G =
`(gR^(2) )/(M)`

If the radius of the earth becomes half,

R =
`(R)/(2)`, then;

G =
`(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 =
`(9.8*(6371000)^(2) )/(4*5.972*10^(24) )`

= 1.670 ×
`10^(-11)`
`m^(3)kg^(-1)s^(-2)`