Question

A particle is projected vertically upward from the surface of earth (radiusRe) with a kinetic energy equal to half of the minimum value needed for it to escape.The height to which it rises above the surface of earth is

A
h=Re
B
h=2Re
C
h=Re/2
D
h=3Re
Solution
Verified by Toppr

The correct option is A h=Re

The kinetic energy needed to escape from the surface is given as,

E=12mve2

=12m(2GmRe)2

=GMmRe

Since, the potential energy at the maximum height will be equal to the sum of half kinetic energy and the potential energy at the surface of the earth.

It can be written as,

GMmRe+12GMmRe=GMmRe+h

12Re=1Re+h

h=Re

The maximum height is Re.

Was this answer helpful?
10
Similar Questions
Q1

The ratio of acceleration due to gravity at a depth (h) below the surface of earth and at a height above the surface of earth for h << Re( radius of earth ):


View Solution
Q2

How much energy is needed to move a body of 103 kg mass from Earth's surface to a height of 2RE?(RE=radius of Earth=6400 km)

View Solution
Q3

The height above the surface of Earth at which gravitational field intensity is reduced to 1% of its value on the surface of Earth is (Re is radius of Earth)

View Solution
Q4

The energy required to take a satellite to a height h above Earth surface (radius of Earth =6.4×103 km) is E1and kinetic energy required for the satellite to be in a circular orbit at this height is E2. The value of h for which E1 and E2 are equal is

View Solution
Q5

A particle is projected vertically upwards from the surface of teh earth (radius Re) with a kinetic energy equal to half of the minimum value needed for it to escape. The height to which it rises above the surface ot the earth is Rn where n is:

View Solution
Solve
Guides