Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Advanced 2025Paper 2
Exam
JEE Advanced
Year
2025
Paper
Paper 2
Subject
Physics
Chapter
Gravitation

JEE Advanced 2025 · Paper 2 · Physics · Gravitation

A geostationary satellite above the equator is orbiting around the...

A geostationary satellite above the equator is orbiting around the earth at a fixed distance r1r_1 from the center of the earth. A second satellite is orbiting in the equatorial plane in the opposite direction to the earth's rotation, at a distance r2r_2 from the center of the earth, such that r1=1.21r2r_1=1.21 r_2. The time period of the second satellite as measured from the geostationary satellite is 24p\frac{24}{p} hours. The value of pp is

Correct answer

0

Step-by-step solution

\mathrm{T} \propto \mathrm{r}^{3 / 2} \frac{\mathrm{T}_2}{\mathrm{ T}_1}=\left(\frac{\mathrm{r}_2}{\mathrm{r}_1}\right)^{3 / 2} \frac{\omega_2}{\omega_1}=\left(\frac{r_1}{r_2}\right)^{3 / 2}=(1.21)^{3 / 2}ω2=ω1(1.331)...(i)(ω2+ω1)t0=2π...(ii)\begin{aligned} & \omega_2=\omega_1(1.331) \qquad ...(i)\\ & \left(\omega_2+\omega_1\right) t_0=2 \pi \qquad ...(ii) \end{aligned}t0=2πω2+ω1=2π(43+1)ω1=6π7ω1t0=6π2π(TGSS)(7)t0=3×24 hours 7=24p hours p=73=2.33t_0=\frac{2 \pi}{\omega_2+\omega_1}=\frac{2 \pi}{\left(\frac{4}{3}+1\right) \omega_1}=\frac{6 \pi}{7 \omega_1} \mathrm{t}_0=\frac{6 \pi}{2 \pi} \frac{\left(\mathrm{ T}_{\mathrm{GSS}}\right)}{(7)} \mathrm{t}_0=\frac{3 \times 24 \text{ hours }}{7}=\frac{24}{\mathrm{p}} \text{ hours } \mathrm{p}=\frac{7}{3}=2.33
Practice Gravitation on Quantrex Academy →

More from Gravitation

A particle of mass m , and angular momentum ℓ is moving in a circular orbit of radius r_0… JEE Advanced 2026A body of mass m is taken from the surface of earth to a height equal to twice the radius… JEE Main 2026When one moves from a point 16 km below the earth's surface to a point 16 km above the… JEE Main 2026The height in terms of radius of the earth (R) , at which the acceleration due to gravity… JEE Main 2026If a body of mass 1 kg falls on the earth from infinity, it attains velocity (v) and… JEE Main 2026A planet (P_1) is moving around the star of mass 2M in the orbit of radius R . Another… JEE Main 2026Three masses 200 ~kg, 300 ~kg and 400 kg are placed at the vertices of an equilateral… JEE Main 2026Given below are two statements: Statement I : A satellite is moving around earth in the… JEE Main 2026 Full Gravitation list All JEE Advanced PYQs