An object is projected vertically up from the earth's surface with velocity √ {Rg} where

English

Gujarati

Hindi

7.Gravitation

hard

An object is projected vertically up from the earth's surface with velocity $\sqrt {Rg}$ where $R$ is the radius of the earth and $'g'$ is the acceleration due to earth on the surface of earth. Find the maximum height reached by the object.

$\frac{R}{2}$

$R$

$2R$

$3R$

Solution

Let the object of mass $\mathrm{m}$ projected with speed

$\mathrm{u}=\sqrt{\mathrm{Rg}}$ reach a height $'h'$ above surface of

earth.

Then from conservation of energy

$\frac{1}{2} m u^{2}-\frac{G M m}{R}=-\frac{G M m}{R+h}$

$\mathrm{u}^{2}=\mathrm{g} \mathrm{R}=\frac{\mathrm{GM}}{\mathrm{R}}$

$\Rightarrow \frac{1}{2} \frac{\mathrm{GMm}}{\mathrm{R}}-\frac{\mathrm{GMm}}{\mathrm{R}}=-\frac{\mathrm{GMm}}{\mathrm{R}+\mathrm{h}}$ or $\mathrm{h}=\mathrm{R}$

Standard 11

Physics

Assuming that the gravitational potential energy of an object at inflinity is zero, the change in potential energy (final-initial) of an object of mass $\mathrm{m}$, when to a height $h$ from the surface of earth (of radius $\mathrm{R}$ ), is given

medium

(NEET-2019)

Two satellites of earth, $S_1$ and $S_2$ are moving in the same orbit. The mass of $S_1$ is four times the mass of $S_2.$ Which one of the following statements is true?

medium

(AIPMT-2007)

A body is projected vertically upwards from the surface of earth with a velocity sufficient enough to carry it to infinity. The time taken by it to reach height $h$ is $….\,S.$

hard

(JEE MAIN-2021)

The masses $m$ in fig. $(A)$ and $(B)$ are identical. The gravitational potential energy in the two cases are $U_A$ and $U_B$. Then

hard

A satellite of mass $m$, initially at rest on the earth, is launched into a circular orbit at a height equal to the radius of the earth. The minimum energy required is

hard

An object is projected vertically up from the earth's surface with velocity $\sqrt {Rg}$ where $R$ is the radius of the earth and $'g'$ is the acceleration due to earth on the surface of earth. Find the maximum height reached by the object.

Solution

Similar Questions

Assuming that the gravitational potential energy of an object at inflinity is zero, the change in potential energy (final-initial) of an object of mass $\mathrm{m}$, when to a height $h$ from the surface of earth (of radius $\mathrm{R}$ ), is given

Two satellites of earth, $S_1$ and $S_2$ are moving in the same orbit. The mass of $S_1$ is four times the mass of $S_2.$ Which one of the following statements is true?

A body is projected vertically upwards from the surface of earth with a velocity sufficient enough to carry it to infinity. The time taken by it to reach height $h$ is $….\,S.$

The masses $m$ in fig. $(A)$ and $(B)$ are identical. The gravitational potential energy in the two cases are $U_A$ and $U_B$. Then

A satellite of mass $m$, initially at rest on the earth, is launched into a circular orbit at a height equal to the radius of the earth. The minimum energy required is

Start a Free Trial Now