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Question

# If g is the acceleration due to gravity at the earth's surface and r is the radius of the earth, the escape velocity for the body to escape out of earth's gravitational field is

A
$$gr$$
B
$$\sqrt{2gr}$$
C
$$\dfrac{g}{r}$$
D
$$\dfrac{r}{g}$$
Solution
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#### Correct option is B. $$\sqrt{2gr}$$Let the mass of the body be $$m$$. When the body will escape earth's gravity into space it will have kinetic and potential energies as zero.$$(KE+PE)_{surface}=(KE+PE)_{space}$$$$\Rightarrow \frac{1}{2}mv_e^2-mgr=0$$ ( $$r$$ is the radius of earth)$$\Rightarrow \frac{1}{2}mv_e^2=mgr$$$$\Rightarrow v_e^2 = 2gr$$.$$\Rightarrow v_e=\sqrt{2gr}$$ is our required answer,

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