Question 1: Gravitation

Question

Find gravitational field at a distance of $$2000 \mathrm{~km}$$ from the centre of earth. (Given
$$R_{	ext {earth }}=6400 \mathrm{~km}, r=2000 \mathrm{~km} 	ext {, } M_{	ext {earth }}=6 	imes 10^{24} \mathrm{~kg} 	ext { ) }$$

Accepted Answer

Given, radius of earth, $$R_e=6400 \mathrm{~km}$$
Distance from centre of earth, $$r=2000 \mathrm{~km}$$
Distance from the surface of earth,
$$\begin{aligned}
d & =R_e-r \
& =6400-2000 \
& =4400 \mathrm{~km}=4.4 	imes 10^6 \mathrm{~m}
\end{aligned}$$
If $$g^{\prime}$$ be the gravitation field below the surface of earth at a depth $$d$$, then
$$\begin{aligned}
g^{\prime} & =g\left(1-\frac{d}{R_{\mathrm{e}}}ight)=9.8\left(1-\frac{4.4 	imes 10^6}{6.4 	imes 10^6}ight) \quad\left[\because g=9.8 \mathrm{~m} / \mathrm{s}^2ight] \
& =9.8 	imes 0.3125=3.06 \mathrm{~m} / \mathrm{s}^2
\end{aligned}$$

Answer

$$1.53 \mathrm{~m} / \mathrm{s}^2$$

Answer

$$7.12 \mathrm{~m} / \mathrm{s}^2$$

Answer

$$3.06 \mathrm{~m} / \mathrm{s}^2$$

Answer

$$1.8 \mathrm{~m} / \mathrm{s}^2$$

Gravitation

Find gravitational field at a distance of $2000 \mathrm{~km} from the centre of earth. (Given R_{\text {earth }}=6400 \mathrm{~km}, r=2000 \mathrm{~km} \text {, } M_{\text {earth }}=6 \times 10^{24} \mathrm{~kg} \text { ) }

Choose the correct answer: