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Gravitation
Gravitational Potential Energy
5 questions, each with its answer.
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With what velocity should a particle be projected so that its height becomes equal to radius of earth -Apply energy conservation between the surface (r = R) and the highest point (r = 2R, where the speed is zero):
$-\dfrac{GMm}{R} + \dfrac{1}{2}mv^2 = -\dfrac{GMm}{2R}$
$\dfrac{1}{2}mv^2 = \dfrac{GMm}{R} - \dfrac{GMm}{2R} = \dfrac{GMm}{2R}$
$v = \sqrt{\dfrac{GM}{R}}$
So the particle must be projected with velocity $\left(\dfrac{GM}{R}\right)^{1/2}$.
That is every 2001 AIPMT question in Gravitational Potential Energy.
Show all 5 questions Next: Gravitational potential energy and work done against gravity
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