Calculate energy needed for moving a mass of 4,,kg from centre of earth to its surface (in

English

Gujarati

Hindi

7.Gravitation

medium

Calculate energy needed for moving a mass of $4\,\,kg$ from the centre of the earth to its surface (in joule), if radius of the earth is $6400\,\, km$ and acceleration due to gravity at the surface of the earth is $g = 10 \,\,m/sec^2.$

A

$1.28 × 10^8 \,\,J$

B

$1.28 × 10^6 \,\,J$

C

$2.56 × 10^8 \,\,J$

D

$2.56 × 10^{10} \,\,J$

Solution

$\mathrm{U}_{\mathrm{i}}=-\frac{3 \mathrm{GMm}}{2 \mathrm{R}}$

$\mathrm{U}_{\mathrm{f}}=\frac{-\mathrm{GMm}}{\mathrm{R}}$

$\Delta \mathrm{U}=\frac{\mathrm{GMm}}{2 \mathrm{R}}=\frac{\mathrm{mgh}}{2}$

$=\frac{4 \times 10 \times 6.4 \times 10^{6}}{2}=1.28 \times 10^{8} \mathrm{J}$

Standard 11

Physics

Share

Similar Questions

The minimum energy required to launch a satellite of mass $m$ from the surface of earth of mass $M$ and radius $R$ in a circular orbit at an altitude of $2 R$ from the surface of the earth is:

medium

(NEET-2024)

A hole is drilled through the earth along a diameter Band a stone is dropped into it. The stone reaches at the centre of the earth, which of the following quantity remains constant

easy

The gravitational potential energy of a body of mass $‘m’$ at the earth’s surface $ – mg{R_e}$. Its gravitational potential energy at a height ${R_e}$ from the earth’s surface will be (Here ${R_e}$ is the radius of the earth)

medium

(AIIMS-2000)

A stationary body on a surface of earth have negative energy -What it indicate (Negative energy indicates that body is bind with earth. If a body give this energy or it will be given positive energy, it goes to at infinity).

medium

To project a body of mass $m$ from earth's surface to infinity, the required kinetic energy is (assume, the radius of earth is $R_E, g=$ acceleration due to gravity on the surface of earth) :

hard

(JEE MAIN-2024)