1) The work done to raise a mass m from the surface of the Earth to a height equal to the radius of the Earth is equal to -mgR/2. 2) The ratio of the escape velocity at Earth (ve) to the escape velocity at a planet with twice the radius and mean density of Earth is 1:√2. 3) A black hole is an object with such a strong gravitational field that not even light can escape from its surface.

1. (lVlalnS ,t,Ul U)
IIGravitational Potential Energy
The work done to raise a mass m from the surface of
the earth to a height h, which is equal to the radius
of the earth, is
3
(a) -mgR
2
(b) mgR
(c) 2mgR
I
(d) -mgR
2
(NEET 2019)

2. D Escape Speed
l. The ratio ofescape velocity at earth (ve) to the escape
velocity at a planet (vP) whose radius and mean
density are twice as that ofearth is
(a) 1:4 (b) l: ✓
2 (c) 1 : 2 (d)l : 2✓
2
(NEET-12016)
>
. A black hole is an object whose gravitational field
is so strong that even light cannot escape from it.

3. 54 The escape velocity from the Earth's surface NEET 2021
is v. The escape velocity from the surface of
another planet having a radius, four times
that of Earth and same mass density is
(a)v (b)2v (c)3v (d) 4v
55 A particle of mass mis projected with a velocity NEET 2021
v = kv,(k < l) from the surface of the Earth.
(Herc, v, = escape velocity)
The maximum height above the surface
reached by the particle is
2 2
(a) R(1~k) (b) R(1: k)
(c) R2k (d) Rk2
1+ k 1-k2

4. (d) We know that, NEET 2021
escape velocity from Eanb's surface, v, = ✓2GM,
where, G is the gravitational constant, Re
Re is the radjus of the Earth,
M, is the mass of the Earth.
. mass
Also, density =---
volume
⇒ Mass =Density x Volume
or M, = p X V
or M, = p X ~ 1t~ ( ·-- V = ~~ )

5. (d) Given, the mass of the particle = m
The velocity of the projected particle, v = kvt
Initial energy at the time of projection
1 2 GMm
= - mv - - -
2 R
Final energy at the maximum heigl1t hfrom surfac(
of the Earth = !. mv1
- GMm
2 R+h
=.!_ m(~l _ GMm
2 R+ h
• 1 • 1 ~ . l r