Question 35: Gravitation

Question

The escape velocity of a projectile on the earth's surface is 11.2 km/s. A body is projected out with thrice this speed. The speed of the body far away from the earth will be

Accepted Answer

By the law of conservation of energy,
$$\begin{aligned}
& (U+K)_{	ext {surface }}=(U+K)_{\infty} \
& \Rightarrow \quad \frac{-G M}{R}+\frac{1}{2} m\left(3 v_eight)^2=0+\frac{1}{2} m v^2 \
& \Rightarrow \quad-\frac{G M}{R}+\frac{9 v_e^2}{2}=\frac{1}{2} v^2 \
& 	ext { Since, } v_e^2=\frac{2 G M}{R} \
& 	herefore \quad \frac{-v_e^2}{2}+\frac{9 v_e^2}{2}=\frac{1}{2} v^2 \
& \Rightarrow \quad v^2=8 v_e^2 \
& v=2 \sqrt{2} v_e=2 \sqrt{2} 	imes 11.2=31.7 \mathrm{~km} / \mathrm{s} \
\end{aligned}$$

Answer

22.4 km/s

Answer

31.7 km/s

Answer

33.6 km/s

Answer

None of these

Gravitation

The escape velocity of a projectile on the earth's surface is 11.2 km/s. A body is projected out with thrice this speed. The speed of the body far away from the earth will be

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