Time period of an artificial satellite in a circular orbit of radius R is 2, days and its

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7.Gravitation

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The time period of an artificial satellite in a circular orbit of radius $R$ is $2\, days$ and its orbital velocity is $v_0$. If time period of another satellite in a circular orbit is $16 \,days$ then

its radius of orbit is $4\,R$ and orbital velocity is $v_0$

its radius of orbit is $4\,R$ and orbital velocity is $\frac{v_0}{2}$

its radius of orbit is $2\,R$ and orbital velocity is $v_0$

its radius of orbit is $2\,R$ and orbital velocity is $\frac{v_0}{2}$

Solution

Using Kepler's law $:$ $\mathrm{T}^{2} \propto \mathrm{R}^{3}$

$\Rightarrow \frac{\mathrm{T}_{1}^{2}}{\mathrm{T}_{2}^{2}}=\frac{\mathrm{R}_{1}^{3}}{\mathrm{R}_{2}^{3}} \Rightarrow \frac{4}{16 \times 16}=\frac{\mathrm{R}^{3}}{\mathrm{R}_{2}^{3}}$

$\Rightarrow \mathrm{R}_{2}=4 \mathrm{R}$

$\frac{\mathrm{V}_{1}}{\mathrm{V}_{2}}=\left(\frac{\mathrm{R}_{2}}{\mathrm{R}_{1}}\right)^{1 / 2} \Rightarrow \mathrm{V}_{2}=\mathrm{V}_{1}\left[\frac{\mathrm{R}_{1}}{\mathrm{R}_{2}}\right]^{1 / 2}$

$\mathrm{V}_{0}=\left[\frac{\mathrm{R}_{1}}{4 \mathrm{R}}\right]^{1 / 2}$

$\mathrm{V}_{2}=\frac{\mathrm{V}_{0}}{2}$

Standard 11

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Solution

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