The escape velocity of a particle of mass m varies as

Q: The escape velocity of a particle of mass m varies as

(a) m2

(b) m

(c) m0

(d) m-1

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Ans: (c)
Sol: Suppose a particle is projected with velocity v from the surface of earth of mass M .

By Energy Conservation ,

$\frac{1}{2}m v^2 + (-\frac{G M m}{R} ) = 0 $

$\frac{1}{2}m v^2 = \frac{G M m}{R} $

$v = \sqrt{\frac{2 G M}{R}} $

It is independent of mass of the particle.