(B) The formula for the time period $T$ of a satellite at a height $h$ above the Earth's surface is given by $T = 2\pi \sqrt{\frac{(R+h)^3}{GM}}$.Sinc

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$4\sqrt 2 \pi \sqrt {\frac{R}{g}} $

(B) The formula for the time period $T$ of a satellite at a height $h$ above the Earth's surface is given by $T = 2\pi \sqrt{\frac{(R+h)^3}{GM}}$.Since $g = \frac{GM}{R^2}$,we can write $GM = gR^2$.Substituting $h = R$ and $GM = gR^2$ into the formula:$T = 2\pi \sqrt{\frac{(R+R)^3}{gR^2}}$$T = 2\pi \sqrt{\frac{(2R)^3}{gR^2}}$$T = 2\pi \sqrt{\frac{8R^3}{gR^2}}$$T = 2\pi \sqrt{\frac{8R}{g}}$$T = 2\pi \cdot 2\sqrt{2} \sqrt{\frac{R}{g}}$$T = 4\sqrt{2}\pi \sqrt{\frac{R}{g}}$.

Class 11 Physics Gravitation Motion of Satellites in Circular Orbits and Planets in Elliptical Orbits

Medium

The periodic time of a satellite revolving above Earth's surface at a height equal to $R$ (where $R$ is the radius of the Earth) is given by (where $g$ is the acceleration due to gravity at Earth's surface):

A
$2\pi \sqrt {\frac{{2R}}{g}} $
B
$4\sqrt 2 \pi \sqrt {\frac{R}{g}} $
C
$2\pi \sqrt {\frac{R}{g}} $
D
$8\pi \sqrt {\frac{R}{g}} $

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Gravitation

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Motion of Satellites in Circular Orbits and Planets in Elliptical Orbits

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MediumAIPMT 1989

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The Earth moves around the Sun in an elliptical orbit as shown in the figure. The ratio $OA/OB = x$. The ratio of the speed of the Earth at $B$ to that at $A$ is nearly

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DifficultAIPMT 1988

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The periodic time of a satellite revolving above Earth's surface at a height equal to $R$ (where $R$ is the radius of the Earth) is given by (where $g$ is the acceleration due to gravity at Earth's surface):

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