SATHEE: Gravitation - Result Question 22

Gravitation - Result Question 22

22. A body weighs $72 N$ on the surface of the earth. What is the gravitational force on it due to earth at a height equal to half the radius of the earth from the surface?

[2000]

(a) $32 N$

(b) $28 N$

(d) $72 N$

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Answer:

Correct Answer: 22. (a)

Solution:

(a) $m g = 72 N$ (body weight on the surface)

$g = \frac{G M}{R^{2}}$

At a height $H = \frac{R}{2}$ ,

$\begin{aligned} g^{'} & = \frac{G M}{(R + \frac{R}{2})^{2}} \\ = \frac{4 G M}{9 R^{2}} \end{aligned}$

Body weight at height $H = \frac{R}{2}$ ,

$\begin{aligned} m g^{'} = m \times \frac{4}{9} (\frac{G M}{R^{2}}) \\ = m \times \frac{4}{9} \times g = \frac{4}{9} m g \\ = \frac{4}{9} \times 72 = 32 N \end{aligned}$

Gravitation - Result Question 22

22. A body weighs $72 N$ on the surface of the earth. What is the gravitational force on it due to earth at a height equal to half the radius of the earth from the surface?

Answer:

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Gravitation - Result Question 22

22. A body weighs 72N on the surface of the earth. What is the gravitational force on it due to earth at a height equal to half the radius of the earth from the surface?

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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22. A body weighs $72 N$ on the surface of the earth. What is the gravitational force on it due to earth at a height equal to half the radius of the earth from the surface?