(B) The orbital velocity of a satellite at height $h$ is given by $v_o = \sqrt{\frac{GM}{R+h}}$. Since $h \ll R$,we can approximate $R+h \approx R$. T

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(B) The orbital velocity of a satellite at height $h$ is given by $v_o = \sqrt{\frac{GM}{R+h}}$. Since $h \ll R$,we can approximate $R+h \approx R$. Thus,$v_o \approx \sqrt{\frac{GM}{R}} = \sqrt{gR}$.The escape velocity from the Earth's surface (or near the surface) is given by $v_e = \sqrt{\frac{2GM}{R}} = \sqrt{2gR}$.The required increase in velocity $\Delta v$ is the difference between the escape velocity and the orbital velocity:$\Delta v = v_e - v_o = \sqrt{2gR} - \sqrt{gR}$.Factoring out $\sqrt{gR}$,we get:$\Delta v = \sqrt{gR}(\sqrt{2} - 1)$.

Class 11 Physics Gravitation Mix Examples-Gravitation

Difficult

$A$ satellite is orbiting the Earth at a height $h$ above the surface (where $R$ is the radius of the Earth and $h \ll R$). What is the minimum increase in the orbital velocity required for the satellite to escape the Earth's gravitational field? (Ignore the effect of the atmosphere.)

A
$\sqrt{\frac{gR}{2}}$
B
$\sqrt{gR}(\sqrt{2}-1)$
C
$\sqrt{2gR}$
D
$\sqrt{gR}$

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Mix Examples-Gravitation

$A$ particle is dropped on Earth from a height $R$ (radius of Earth) and it bounces back to a height $R/2$. The coefficient of restitution for the collision is (ignore air resistance and rotation of Earth).

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$A$ star of mass $M$ and radius $R$ is made up of gases. The average gravitational pressure compressing the star due to the gravitational pull of the gases making up the star depends on $R$ as

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$A$ 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.

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How many times is the escape velocity $(V_e)$ of the orbital velocity $(V_0)$ for a satellite revolving near the Earth?

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Three identical particles $A, B$,and $C$ of mass $100 \, kg$ each are placed in a straight line with $AB = BC = 13 \, m$. The gravitational force on a fourth particle $P$ of the same mass is $F$,when placed at a distance $13 \, m$ from the particle $B$ on the perpendicular bisector of the line $AC$. The value of $F$ will be approximately $....G$.

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$A$ satellite is orbiting the Earth at a height $h$ above the surface (where $R$ is the radius of the Earth and $h \ll R$). What is the minimum increase in the orbital velocity required for the satellite to escape the Earth's gravitational field? (Ignore the effect of the atmosphere.)

Similar Questions

$A$ particle is dropped on Earth from a height $R$ (radius of Earth) and it bounces back to a height $R/2$. The coefficient of restitution for the collision is (ignore air resistance and rotation of Earth).

$A$ star of mass $M$ and radius $R$ is made up of gases. The average gravitational pressure compressing the star due to the gravitational pull of the gases making up the star depends on $R$ as

$A$ 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.

How many times is the escape velocity $(V_e)$ of the orbital velocity $(V_0)$ for a satellite revolving near the Earth?

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