Question

Assuming earth to be a sphere of uniform mass density, how much would a body wrigh galf way down the centre of rhe centre of the earth , if it weighed 100 N on the surface?

Answer 1

The weight of the body will be 50 N.

We have to find out how much the body will weigh half way down the surface of the earth.

• Weight of body on earth = 100 N

        mg° = 100

        m = 100/g° ....(1)

• Acceleration due to gravity varies with depth as,

        g = g°. [1 - $\frac{d}{R}$ ] where g° is acc. due to gravity on earths      surface and d is the depth.

        We are given d = R/2

• g = g° . [ 1 - $\frac{\frac{R}{2} }{R}$ ]
• g = g°/2 ....(2)
• The weight of the body will be mg.
• mg = (100/g°)×(g°/2)
• mg = 50 N

Answer 2

Hence the weight of the object is 50 N.

Explanation:

We have to find out how much the body will weigh half way down the surface of the earth.

Weight of body on earth = 100 N

mg = 100

m = 100/g     -------(1)

Acceleration due to gravity varies with depth as,

g = go.

Where g° is acceleration due to gravity on earth's surface and d is the depth.

We are given d = R/2

g = g° . [ 1 -]

g = go/2  ---------(2)

The weight of the body will be mg.

mg = (100/go)×(go/2) = 50 N

Hence the weight of the object is 50 N