Question 4: Gravitation

Question

The weight of a body on the surface of the
earth is 63 N. What is the gravitational force
on it due to the earth at a height equal to
half the radius of the earth?

Accepted Answer

Given, $$h=\frac{R_e}{2}$$
Acceleration due to gravity at altitude $$h$$ is given by
$$\begin{aligned}
g^{\prime} & =\frac{g}{\left(1+\frac{h}{R_e}ight)^2}=\frac{g}{\left(1+\frac{R_e / 2}{R_e}ight)^2} \
& =\frac{g}{\left(1+\frac{1}{2}ight)^2}=\frac{g}{\left(\frac{3}{2}ight)^2}=\frac{4 g}{9} \quad 	ext{.... (i)} 
\end{aligned}$$
Weight of the body at the earth's surface,
$$w=m g=63 \mathrm{~N}$$ .... (ii)
Weight of the body at altitude, $$h=\frac{R_e}{2}$$
$$w^{\prime}=m g^{\prime}=\frac{4}{9} m g$$ ..... (iii)
Using Eq. (ii), we get
$$w^{\prime}=\frac{4}{9} 	imes 63=28 \mathrm{~N}$$

Answer

35 N

Answer

28 N

Answer

18 N

Answer

40 N

Gravitation

The weight of a body on the surface of the earth is 63 N. What is the gravitational force on it due to the earth at a height equal to half the radius of the earth?

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