Question

how deep a mine should be dug so that the weight of a body decreases by 75% as that on surface of the earth​

Answer 1

Let suppose x height below from earth surface, a mine should be dug so that the weight of body decrease by 75%.

• Under a depth x from earth surface , acceleration due to gravity is ģ = g(1-x÷R). Where R is radius of earth and g is acceleration due to gravity at earth surface.
• Since weight is decreased by 75% , it means 25% of weight is acting on that.
• mģ = mg × 25/100
• mg(1- x÷R) = mg ×25/100
• (1-x÷R ) = 1÷4

Hence x = 3R/4

So, the mine should be dug upto 3/4 0f radius of earth below the earth surface