Question

Choose the correct alternative: 

1. Acceleration due to gravity increases/decreases with increasing altitude. 

2. Acceleration due to gravity increases/decreases with increasing depth (assume the earth to be a sphere of uniform density). 

3. Acceleration due to gravity is independent of the mass of the earth/ mass of the body. 

4. The formula – G Mm(1/r₂ – 1/r₁) is more/less accurate than the formula mg(r₂ – r₁) for the difference of potential energy between two points r₂ and r₁ distance away from the centre of the earth.

Answer 1

1. Decreases. 

The value of acceleration due to gravity at a height ‘h’ above the ground ‘gh’ is given by, g_h =g[1-2h/R_e] where Re is radius of Earth. Therefore g_h decreases with an increase in height.

2. Decreases. 

The value of acceleration due to gravity at a depth ‘d’ below the ground (g_d), is given by, g_d =gh =g[1-2h/R_e] where Re is the radius of earth. This shows that with an increase in the value of ‘d’ i the value of g_d decreases.

3. Mass of the body. 

The acceleration due to gravity of any planet of mass ‘M’ and radius ‘R’ is given by, g = GM/R², where, G is the universal gravitational constant. So, the value of ‘g’ is dependent on the mass of the earth but independent of mass of the body.

4. More accurate.

 The gravitational potential energy of any point at a distance ‘r’ from the centre of the earth is V (r) = GmM/r

So, Potential Energy difference

= gm (r₂ – r₁)

= mgr₂ – mgr₁

(Assuming r₂ – r₁ ≈ R² )

Thus -GmM (1/r₂ -1/r₂) is a more accurate relation.