A satellite of mass m is at a distance of 'a' from a star of mass M. speed of the satel

English

Gujarati

Hindi

7.Gravitation

hard

A satellite of mass m is at a distance of $'a'$ from a star of mass $M.$ The speed of the satellite is $u.$ Suppose the law of universal gravity is $F=-G\frac{Mm}{r^{2.1}}$ instead of $F=-G\frac{Mm}{r^{2}}$ find the speed of the satellite when it is at $a$ distance $b$ from the star.

A

$\sqrt{u^2+2GM(\frac{1}{b^{1.1}}-\frac{1}{a^{1.1}})}$

B

$\sqrt{u^2+\frac{2}{1.1}GM(\frac{1}{b^{1.1}}-\frac{1}{a^{1.1}})}$

C

$\sqrt{u^2+\frac{2}{2.1}GM(\frac{1}{b^{1.1}}-\frac{1}{a^{1.1}})}$

D

$\sqrt{u^2+\frac{2}{1.1}GM(\frac{1}{b}-\frac{1}{a})}$

Solution

$\Sigma \mathrm{W}_{\mathrm{F}}=\Delta \mathrm{K}(\mathrm{WET})$

$\int_{a}^{b} \frac{-G M}{r^{2-1}} d r=\frac{1}{2} m v^{2}-\frac{1}{2} m u^{2}$

$\frac{\mathrm{GM}}{1.1}\left[\frac{1}{\mathrm{a}^{1.1}}-\frac{1}{\mathrm{b}^{1.1}}\right]=\frac{1}{2} \mathrm{mv}^{2}-\frac{1}{2} \mathrm{mu}^{2}$

Standard 11

Physics

Share

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

medium

(NEET-2019)

A body is released from a height equal to the radius ( $R$ ) of the earth. The velocity of the body when it strikes the surface of the earth will be :

(Given $g$ = acceleration due to gravity on the earth.)

medium

(JEE MAIN-2023)

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

Two masses $m_1$ and $m_2$ are at rest a infinity. Find their relative velocity of approach due to gravitational attraction when their separation is $d$

medium

If one wants to remove all the mass of the earth to infinity in order to break it up completely. The amount of energy that needs to be supplied will be $\frac{x}{5}\, \frac{ GM ^{2}}{ R }$ where $x$ is $\quad\,……….$ (Round off to the Nearest Integer)

($M$ is the mass of earth, $R$ is the radius of earth, $G$ is the gravitational constant)

hard

(JEE MAIN-2021)