Question

While sitting on the surface of the Earth, a satellite has a weight of 1600 N.  This satellite is put into orbit so that it is four times the distance from the center of the Earth as it had been while on the surface of the Earth. What will happen to the weight of the satellite?

	A.	The weight of the satellite will be reduced to 1/2 of its original, making it weigh 800 N.
	B.	The weight of the satellite will be reduced to 1/16 of its original, making it weigh100 N.
	C.	The weight of the satellite will be increased to twice its original, making it weigh 3200 N.
	D.	The weight of the satellite will be reduced to 1/4 of its original, making it weigh 400 N.

Answer 1

The correct option is (B) The weight of the satellite will be reduced to 1/16 of its original, making it weigh100 N.

Explaination :-

weight on the surface of earth,

W = 1600 N

which is equal to the Gravitational force between the earth and the satellite.

W = G*M*m/r² ---------->(1)

where r is the distance between earth and satellite.

now r is increased to 4r.

so the new weight is,

Wn = G*M*m/(4*r)²

16 * Wn= G*M*m/r²

using equation (1)

16*Wn = 1600

Wn = 100 N.

or

as we have seen the weight (gravitational force) is inversely proportional to the square of the distance between them.so, distance is increased by 4 times than the weight is decreased by 16 times.