Single Choice

EARTH SATELLITE The time period T of the moon of planet mars (mass $$M_{m}$$) is related to its orbital radius R as (G= Gravitational constant)

A$$T^{2}=\dfrac{4{\pi}^{2}R^{3}}{GM_{m}}$$
Correct Answer
B$$T^{2}=\dfrac{4{\pi}^{2}GR^{3}}{M_{m}}$$
C$$T^{2}=\dfrac{2\pi{R^{3}}G}{M_{m}}$$
D$$T^{2}=4{\pi}M_{m}GR^{3}$$

Solution

Time period $$T=\dfrac { 2\pi }{ { V }_{ 0 } } $$
$$T=\dfrac { 2\pi R }{ \sqrt { { GM }_{ m } } } \quad \left( ={ V }_{ 0 }=\sqrt { \dfrac { GM }{ R } } \right) $$
$${ T }^{ 2 }=\dfrac { 4{ \pi }^{ 2 }{ R }^{ 3 } }{ { GM }_{ m } } $$

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