Question

3. The acceleration due to gravity is independent of;

a) Mass of the earth b) Mass of the object

c) Radius of the earth d) Height of the object from the surface of the earth ​

Answer 1

Mass of the object ....

mass

Acceleration due to gravity is independent of mass. These two quantities are independent of each other. Light objects accelerate more slowly than heavy objects when force other then gravity are also at work.

Answer 2

Answer:

(a) Acceleration decreases according to formula g

′

=g(1−

R

2h

),

where h is height and R is radius of earth.

(b) Acceleration decreases according to formula g

′

=g(1−

R

d

),

where d is depth and R is radius of earth.

(c) Acceleration due to gravity is given by the formula: g=

R

e

2

GM

e

Hence, it is independent of mass of body, but is dependent on mass of earth.

(d) Gravitational potential energy is given by the formula: U=−

r

Gm

1

m

2

g=

R

e

2

GM

e

assuming distance between object and earth is nearly equal to the radius of the earth.

Substituting the second equation in first, we get U≈mgh

Hence, the first formula is more accurate.