Gravitational Forces - Questions

Question

1. Indicate which statement is true(T) or false(F)? If false then change the word or phrase that is bold and underlined to make it true.

___The acceleration of gravity experienced by objects located near to (and far from) the earth depends upon the mass of the Earth.

___Increasing the mass of an object will increase the acceleration of gravity experienced by the object.

___Doubling the distance between an object and the earth’s center will decrease the acceleration of gravity by a factor of two.

___If the mass of the Earth were doubled, then the acceleration of gravity on its surface would be quadrupled.

___If the mass of the Earth were quadrupled and the radius of the earth were doubled then the two changes would offset each other and the acceleration of gravity would remain the same.

2. Two spherical balls are placed so their centers are 255 cm apart. The force between the two balls is 2.80 x 10-12 N. What is the mass of each ball if one ball is 3.00 kg more than the mass of the other ball?

Answer 1

H Hussain:

Here we go:

Part 1:

1. True
2. False: underlined s/be will not (All objects experience the same gravitational acceleration due to the Earth
3. True
4. False: underlined s/be doubled
5. True

Part 2: Let the mass of the smaller ball be m => mass of the larger ball is 3m

The gravitational force between the two balls is given by Newton's Law of Gravitation, where the force is in Newtons and distance is in meters.

=> G m (3m) / 2.55² = 2.8 x 10^-12 where G = universal gravitational constant

=> G 3m² = 2.8 10^-12 x 2.55²

=> m² = 2.8 10^-12 x 2.55²/ (3 G) and

=> m = √( (2.8 x 2.55² x 10^-1) / (3 x 6.67430) )

= 0.301 kg