Figure shows orbit of a planet P round sun S. AB and CD are minor and major axes of ellipse. If U is

English

Gujarati

Hindi

7.Gravitation

medium

Figure shows the orbit of a planet $P$ round the sun $S.$ $AB$ and $CD$ are the minor and major axes of the ellipse.

If $U$ is the potential energy and $K$ kinetic energy then $|U| > |K|$ at

A

Only $D$

B

Only $C$

C

both $D\ \& \ C$

D

neither $D$ nor $C$

Solution

At any point, $P . E .=\frac{-G M m}{a}$ and

$K . E .=\frac{G M m}{2 a}$

Now $|P . E .|=\frac{G M m}{a}$ and $|K . E .|=\frac{G M m}{2 a}$

We can clearly observe that $|P . E .|=2|K . E .| \Rightarrow|U|>|K|$ at $D$ and $C.$

Standard 11

Physics

Share

Similar Questions

Given below are two statements:

Statement $I:$ If $E$ be the total energy of a satellite moving around the earth, then its potential energy will be $\frac{E}{2}$.

Statement $II:$ The kinetic energy of a satellite revolving in an orbit is equal to the half the magnitude of total energy $E$.

In the light of the above statements, choose the most appropriate answer from the options given below

medium

(JEE MAIN-2023)

The curves for potential energy $(U)$ and kinetic energy $({E_k})$ of a two particle system are shown in figure. At what points the system will be bound?

easy

If the gravitational acceleration at surface of Earth is $g,$ then increase in potential energy in lifting an object of mass $m$ to a height equal to half of radius of earth from surface will be

hard

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

An astronaut takes a ball of mass $m$ from earth to space. He throws the ball into a circular orbit about earth at an altitude of $318.5 \mathrm{~km}$. From earth's surface to the orbit, the change in total mechanical energy of the ball is $x \frac{\mathrm{GM}_e \mathrm{~m}}{21 R_e}$. The value of $x$ is (take $R_{\mathrm{e}}=6370 \mathrm{~km}$ ):

hard

(JEE MAIN-2024)