Question

The weight of an object in the coal mine, sea level and at the top of the mountain, are respectively W₁, W₂, and W₃, then
1. W1 < W2 < W3
2. W₁ > W₂ > W₃
3. W1 = W2 = W3
4. W1 < W2 > W3

Answer 1

Correct Answer - Option 4 : W1 < W2 > W3

CONCEPT:

Acceleration due to Gravity:

• The force of attraction exerted by the earth on a body is called gravitational pull or gravity.
• We know that when a force acts on a body, it produces acceleration. Therefore, a body under the effect of gravitational pull must accelerate.

• Acceleration due to the gravity of earth having mass M on the surface of the earth is given by:

\(⇒ g = \;\frac{{GM}}{{{R^2}}}\)     ------ (1)

• Variation in g with depth is given by:

\(⇒ g' = g\left[ {1 - \frac{d}{{R}}} \right]\)     ------ (1)

Where is the g’ = Acceleration due to gravity at depth d, R = Radius of the earth and g = Acceleration due to gravity at the surface of the earth.

• Acceleration due to gravity at height h from the surface of the earth -

\(⇒ g' = \frac{{GM}}{{{{\left( {R + h} \right)}^2}}}\)      ----(3)

EXPLANATION:

• Variation in g with depth is given by 

\(⇒ g' = g\left[ {1 - \frac{d}{R}} \right]\)

• From the above equation, it is clear that the value of g decreases on going below the surface of the earth.

• From equation 3 it is clear that the value of g decreases on going above the surface of the earth.
  • So it is clear that if h increases, the value of g decreases. It is inversely proportional to the square of the distance from the center of the earth i.e. (R + h)2.
• At the surface of the earth, the value of g = 9.8m/sec². If we go towards the centre of the earth or we go above the surface of the earth, then in both cases the value of g decreases.
• As we know the weight of the body is given by

⇒ W = mg

• So as g decreases on going below the surface of the earth or we go above the surface of the earth. Therefore, its weight also decreases. Hence, 

⇒ W₁ = mg_mine

⇒ W2 = mg_{sea level}

⇒ W3 = mg_mountain

So, W1 < W2 > W3

Mass	Weight
Mass of a body is the measure of its inertia, greater the mass of the body greater will be the inertia	The weight of a body at any place is the product of its mass and gravitational acceleration at that place. W = mg
Mass of the body always remains constant.	The weight of the body can slightly vary from place to place on the earth.
Its value can never be zero for any material particle.	At the pole, the weight of the body is maximum, whereas at the equator, it is minimum.