Question

If g₁ and g₂ are the gravitational acceleration on two mountains A and B respectively, then the weight of body when transported from A to B will be multiplied by
1. Factor g₁
2. Factor g₂
3. Factor (g₁/g₂)
4. Factor (g₂/g₁)

Answer 1

Correct Answer - Option 4 : Factor (g₂/g₁)

Concept:

Mass (m):

The most basic measure of the matter which represents its linear inertia is known as mass

SI = kg [M¹L⁰T⁰]

Weight (W):

The force of gravity acting on a body is known as the weight of that body.

SI = N [M¹L¹T^-2]

The relation between mass and weight is given by

W = m × g

Where g = gravitational acceleration = 9.81 m/sec²

Calculation:

Given:

g₁ and g₂ are the gravitational acceleration on two mountains A and B respectively

So let us assume the weight of a body on-mountain A and B are W₁ and W₂ respectively

W₁ = m × g₁

W₂ = m × g₂

Taking the ratio of w₂ and W₁

\(\frac{{{{\rm{W}}_2}}}{{{{\rm{W}}_1}}} = \frac{{{\rm{m}} \times {{\rm{g}}_2}}}{{{\rm{m}} \times {{\rm{g}}_1}}}\)

\({{\rm{W}}_2} = {{\rm{W}}_1} \times \frac{{{{\rm{g}}_2}}}{{{{\rm{g}}_1}}}\)

Hence the weight of the body when it is moved from mountain A to mountain B is multiplied by a factor (g₂/g₁)