The time period T of the moon of planet mars (mass Mm) is related to its orbital radius R (G = Gravitational constant) as

Question

The time period T of the moon of planet mars (mass Mm) is related to its orbital radius R (G = Gravitational constant) as (A) T2=(4π2R3/GMm) (B) T2=(4π2GR3/Mm) (C) T2=(2π R3G/Mm) (D) T2=4π MmGR3

Tardigrade Admin · Accepted Answer

Time period T=(2π r/vo) T=(2π R/√GMm) (∴ vo=√(GM/R)) T2=(4π2R3/GMm)

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

$T^{2} = \frac{4 π ^{2} R ^{3}}{G M _{m}}$

$T^{2} = \frac{4 π ^{2} G R ^{3}}{M _{m}}$

$T^{2} = \frac{2 π R ^{3} G}{M _{m}}$

$T^{2} = 4 π M_{m} G R^{3}$

Time period $T = \frac{2 π r}{v _{o}}$
$T = \frac{2 π R}{G M _{m}}$ $(∴ v_{o} = \frac{GM}{R})$
$T^{2} = \frac{4 π ^{2} R ^{3}}{G M _{m}}$

Q. The time period T of the moon of planet mars (mass Mm​) is related to its orbital radius R (G = Gravitational constant) as

T2=GMm​4π2R3​

T2=Mm​4π2GR3​

T2=Mm​2πR3G​

T2=4πMm​GR3

Time period T=vo​2πr​ T=GMm​​2πR​ (∴vo​=RGM​​) T2=GMm​4π2R3​