JEE MAIN - Physics (2021 - 27th July Evening Shift - No. 16)
The planet Mars has two moons, if one of them has a period 7 hours, 30 minutes and an orbital radius of 9.0 $$\times$$ 103 km. Find the mass of Mars.
$$\left\{ {Given\,{{4{\pi ^2}} \over G} = 6 \times {{10}^{11}}{N^{ - 1}}{m^{ - 2}}k{g^2}} \right\}$$
$$\left\{ {Given\,{{4{\pi ^2}} \over G} = 6 \times {{10}^{11}}{N^{ - 1}}{m^{ - 2}}k{g^2}} \right\}$$
5.96 $$\times$$ 1019 kg
3.25 $$\times$$ 1021 kg
7.02 $$\times$$ 1025 kg
6.00 $$\times$$ 1023 kg
Explanation
Option D is correct.
$${T^2} = {{4{\pi ^2}} \over {GM}}.{r^3}$$
$$M = {{4{\pi ^2}} \over G}.{{{r^3}} \over {{T^2}}}$$
by putting values
$$M = 6 \times {10^{23}}$$
$${T^2} = {{4{\pi ^2}} \over {GM}}.{r^3}$$
$$M = {{4{\pi ^2}} \over G}.{{{r^3}} \over {{T^2}}}$$
by putting values
$$M = 6 \times {10^{23}}$$
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