Question

The radius of the earth is about 6370 km. An object of mass 30 kg is taken to a height of 230 km above the surface of earth.
(a) What is the mass of the body?
(b) What is the acceleration due to gravity at this height?
(c) What is the weight of the body at this height?

Answer 1

(a) Since the mass of a body is independent of its location and does not vary with the gravitational force, therefore, the mass of the body at 230 km above the surface of the earth is 30 kg.

(b) We know that,

Acceleration due to gravity, $g=\frac{G{m}_1}{R^2}$

Where m₁ is mass of earth.

$g=\frac{6.673\times {10}^{-11}\times 5.97\times {10}^{24}}{{\left(\right(230+6370\left)\right(1000\left)\right)}^2}$

$\therefore$ Acceleration due to gravity $g=9.14$ $\frac{m}{{sec}^2}$

(c) Weight of body = $massofbody\times accelerationduetogravity$

$=(30\times 9.14)$

$=274.2N$.