1
JEE Advanced 2025 Paper 2 Online
MCQ (Single Correct Answer)
+3
-1

Consider a star of mass m2 kg revolving in a circular orbit around another star of mass m1 kg with m1 \gg m2. The heavier star slowly acquires mass from the lighter star at a constant rate of $\gamma$ kg/s. In this transfer process, there is no other loss of mass. If the separation between the centers of the stars is r, then its relative rate of change $\frac{1}{r}\frac{dr}{dt}$ (in s−1) is given by:

A

$-\frac{3\gamma}{2m_{2}}$

B

$-\frac{2\gamma}{m_{2}}$

C

$-\frac{2\gamma}{m_{1}}$

D

$-\frac{3\gamma}{2m_{1}}$

2
JEE Advanced 2024 Paper 2 Online
MCQ (Single Correct Answer)
+3
-1

A particle of mass $m$ is under the influence of the gravitational field of a body of mass $M(\gg m)$. The particle is moving in a circular orbit of radius $r_0$ with time period $T_0$ around the mass $M$. Then, the particle is subjected to an additional central force, corresponding to the potential energy $V_{\mathrm{c}}(r)=m \alpha / r^3$, where $\alpha$ is a positive constant of suitable dimensions and $r$ is the distance from the center of the orbit. If the particle moves in the same circular orbit of radius $r_0$ in the combined gravitational potential due to $M$ and $V_{\mathrm{c}}(r)$, but with a new time period $T_1$, then $\left(T_1^2-T_0^2\right) / T_1^2$ is given by

[G is the gravitational constant.]

A
$\frac{3 \alpha}{G M r_0^2}$
B
$\frac{\alpha}{2 G M r_0^2}$
C
$\frac{\alpha}{G M r_0^2}$
D
$\frac{2 \alpha}{G M r_0^2}$
3
JEE Advanced 2023 Paper 1 Online
MCQ (Single Correct Answer)
+3
-1
Two satellites $\mathrm{P}$ and $\mathrm{Q}$ are moving in different circular orbits around the Earth (radius $R$ ). The heights of $\mathrm{P}$ and $\mathrm{Q}$ from the Earth surface are $h_{\mathrm{P}}$ and $h_{\mathrm{Q}}$, respectively, where $h_{\mathrm{P}}=R / 3$. The accelerations of $\mathrm{P}$ and $\mathrm{Q}$ due to Earth's gravity are $g_{\mathrm{P}}$ and $g_{\mathrm{Q}}$, respectively. If $g_{\mathrm{P}} / g_{\mathrm{Q}}=36 / 25$, what is the value of $h_{\mathrm{Q}}$ ?
A
$\frac{3 R}{5}$
B
$\frac{R}{6}$
C
$\frac{6 R}{5}$
D
$\frac{5 R}{5}$
4
JEE Advanced 2019 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
Consider a spherical gaseous cloud of mass density $$\rho $$(r) in free space where r is the radial distance from its center. The gaseous cloud is made of particles of equal mass m moving in circular orbits about the common center with the same kinetic energy K. The force acting on the particles is their mutual gravitational force. If $$\rho $$(r) is constant in time, the particle number density n(r) = $$\rho $$(r)/m is [G is universal gravitational constant]
A
$${K \over {6\pi {r^2}{m^2}G}}$$
B
$${K \over {\pi {r^2}{m^2}G}}$$
C
$${3K \over {\pi {r^2}{m^2}G}}$$
D
$${K \over {2\pi {r^2}{m^2}G}}$$
JEE Advanced Subjects