Q.30. A planet (P) is moving around the star of mass in the orbit of radius . Another planet (P) is

Q: What is the correct answer for JEE Main Physics Q30?

The correct answer is B. Sol. From Kepler's third law, the square of the orbital period $T$ is proportional to the cube of the semi-major axis $r$ and inversely proportional to the mass of the central star $M_s$. $T^2 = \frac{4\pi^2}{GM_s} r^3 \Rightarrow T \propto \frac{r^{3/2}}{\sqrt{M_s}}$ For planet P$_1$: Mass of star $M_{s1} = 2M$ Orbital radius $r_1 = R$ Time period $T_1 \propto \frac{R^{3/2}}{\sqrt{2M}}$ For pla

Q: Q.30. A planet (P) is moving around the star of mass in the orbit of radius . Another planet (P) is moving around another star of mass in a orbit of radius . Ratio of time periods of revolution of…

The correct answer is B. Sol. From Kepler's third law, the square of the orbital period $T$ is proportional to the cube of the semi-major axis $r$ and inversely proportional to the mass of the central star $M_s$. $T^2 = \frac{4\pi^2}{GM_s} r^3 \Rightarrow T \propto \frac{r^{3/2}}{\sqrt{M_s}}$ For planet P$_1$: Mass of star $M_{s1} = 2M$ Orbital radius $r_1 = R$ Time period $T_1 \propto \frac{R^{3/2}}{\sqrt{2M}}$ For pla

Q: What are the options for this JEE Main Physics question?

A. $\frac{1}{2}$ · B. 2 · C. 4 · D. $\frac{1}{4}$

Question

Q.30. A planet (P) is moving around the star of mass  in the orbit of radius . Another planet (P) is moving around another star of mass  in a orbit of radius . Ratio of time periods of revolution of P and P is

FirstInTest · Accepted Answer

Sol. From Kepler's third law, the square of the orbital period $T$ is proportional to the cube of the semi-major axis $r$ and inversely proportional to the mass of the central star $M_s$.
$T^2 = \frac{4\pi^2}{GM_s} r^3 \Rightarrow T \propto \frac{r^{3/2}}{\sqrt{M_s}}$

For planet P$_1$:
Mass of star $M_{s1} = 2M$
Orbital radius $r_1 = R$
Time period $T_1 \propto \frac{R^{3/2}}{\sqrt{2M}}$

For planet P$_2$:
Mass of star $M_{s2} = 4M$
Orbital radius $r_2 = 2R$
Time period $T_2 \propto \frac{(2R)^{3/2}}{\sqrt{4M}} = \frac{2^{3/2} R^{3/2}}{2\sqrt{M}} = \frac{2\sqrt{2} R^{3/2}}{2\sqrt{M}} = \frac{\sqrt{2} R^{3/2}}{\sqrt{M}}$

Now, we need the ratio of time periods of revolution of P$_2$ and P$_1$, i.e., $\frac{T_2}{T_1}$:
$\frac{T_2}{T_1} = \frac{\frac{\sqrt{2} R^{3/2}}{\sqrt{M}}}{\frac{R^{3/2}}{\sqrt{2M}}} = \frac{\sqrt{2} R^{3/2}}{\sqrt{M}} 	imes \frac{\sqrt{2M}}{R^{3/2}} = \frac{\sqrt{2}}{\sqrt{M}} 	imes \sqrt{2M} = \sqrt{2} 	imes \sqrt{2} = 2$.

So, $\frac{T_2}{T_1} = 2$.

Answer

$\frac{1}{2}$

Answer

2

Answer

4

Answer

$\frac{1}{4}$

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