96. Show that if a body be projected vertically upward from the surface of the earth so as to reach a height nR above the surface i) the increase in its potential energy is (n/n+1)mgR ii) the velocity with which it must be projected is \sqrt{}(2ngR/n+1), where R is the radius of the earth and m the mass of body

Open in App

Solution

Suggest Corrections

Similar questions

Q. If a body be projected vertically upward from the surface of the earth so as to reach a height

n R

above the surface; the increase in its potential energy is

(\frac{n}{n + a}) m g R

,where

a =

Q. The velocity with which it must be projected is

\sqrt{\frac{2 n g R}{n + 1}}

,where

R

is the radius of the earth and

m

the mass of body.

Q. A particle is projected vertically upwards from the surface of teh earth (radius

R_{e}

) 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

\frac{R}{n}

where

n

is:

Q. A body is projected horizontally from the surface of the Earth

(r a d i u s = R)

with a velocity equal to

n

times the escape velocity. Neglect rotational effects of the earth. The maximum height attained by the body from the earth's surface is

R / 2

. Then

n

must be

A body is projected vertically upwards from the surface of the earth with a velocity sufficient to carry it to infinity. If the radius of the earth is R, the velocity of the body at a height h is

Join BYJU'S Learning Program