1
JEE Advanced 2023 Paper 1 Online
+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
$\frac{5 R}{5}$
2
JEE Advanced 2019 Paper 1 Offline
+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
$${K \over {2\pi {r^2}{m^2}G}}$$
3
JEE Advanced 2018 Paper 2 Offline
+3
-0.75
A planet of mass $$M,$$ has two natural satellites with masses $${m_1}$$ and $${m_2}.$$ The radii of their circular orbits are $${R_1}$$ and $${R_2}$$ respectively, Ignore the gravitational force between the satellites. Define $${v_1},{L_1},{K_1}$$ and $${T_1}$$ to be , respectively, the orbital speed, angular momentum, kinetic energy and time period of revolution of satellite $$1$$; and $${v_2},{L_2},{K_2},$$ and $${T_2}$$ to be the corresponding quantities of satellite $$2.$$ Given $${m_1}/{m_2} = 2$$ and $${R_1}/{R_2} = 1/4,$$ match the ratios in List-$${\rm I}$$ to the numbers in List-$${\rm II}.$$

LIST - I LIST - II
P. v1/v2 1. 1/8
Q. L1/L2 2. 1
R. K1/K2 3. 2
S. T1/T2 4. 8
A
$$P \to 4;Q \to 2;R \to 1;S \to 3$$
B
$$P \to 3;Q \to 2;R \to 4;S \to 1$$
C
$$P \to 2;Q \to 3;R \to 1;S \to 4$$
D
$$P \to 2;Q \to 3;R \to 4;S \to 1$$
4
JEE Advanced 2017 Paper 2 Offline
+3
-0.75
A rocket is launched normal to the surface of the Earth, away from the sun, along the line joining the Sun and the Earth. The Sun is $$3 \times 10{}^5$$ times heavier than the earth and is at a distance $$2.5 \times {10^4}$$ times larger than the radius of the Earth. The escape velocity from Earth's gravitational field is $${V_c} = 11.2km\,{s^{ - 1}}.$$. The minimum initial velocity $$\left( {{v_s}} \right)$$ required for the rocket to be able to leave the sun-earth system is closest to (Ignore the the rotation and revoluation of the earth and the presence of any other planet) $${v_s} = 72km{s^{ - 1}}$$
A
$${v_s} = 22\,km\,{s^{ - 1}}$$
B
$${v_s} = 42\,km\,{s^{ - 1}}$$
C
$${v_s} = 62km\,{s^{ - 1}}$$
D
$${v_s} = 72km{s^{ - 1}}$$
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