at what depth from the surface of the earth will a body of mass 5 kg experience the same force as at a height of R/3 above the earths surface? assume the earth to be a uniform sphere of radius R.

Open in App

Solution

Dear student

The force on a body of mass m is given by mg. where g is the acceleration due to gravity. the value of g changes with the height and depth.
$T h e v a l u e o f g a t a d e p t h x = g (1 - \frac{x}{R}) a n d a t h e i g h t h t h e v a l u e o f g, = \frac{g}{{(1 + \frac{h}{R})}^{2}} f o r h < < R i t i s = g (1 - \frac{2 h}{R}) s o a c c o r d i n g t o t h e q u e s t i o n h = \frac{R}{3} f o r c e o n b o d y a t h e i g h t h = f o r c e o n b o d y a t a d e p t h x m \times g a t h e i g h t h = m \times g a t d e p t h x g (1 - \frac{2 h}{R}) = g (1 - \frac{x}{R}) 1 - \frac{2}{3} = 1 - \frac{x}{R} x = \frac{2}{3} R$

Suggest Corrections

Similar questions

Q. Assuming the earth to be a sphere of uniform density how much could a body weigh at a depth one third of radius of earth. from the surface of earth, when the body weight 300 N on the surface of earth.?

A body weighs $72 N$ on the surface of the earth. What will be the force of gravity acting on the body at a height equal to half the radius of the earth above the earth's surface?

Q. The gravitational force on a body of mass

5 k g

at the surface of the earth is

50 N

. If earth is a perfect sphere, the gravitational force on a satellite of mass

200 k g

in a circuit orbit of radius same as diameter of the earth is.

Q. Assuming the earth to be a sphere of uniform density, how much could a body weigh at a height equal to radius of earth when it weighs 250 N on the surface of the earth.

Q. A man weighs

80 k g

on the surface of earth of radius

R

. At what height above the surface of earth his weight will be

40 k g

Join BYJU'S Learning Program