List of top Physics Questions on Gravitation asked in JEE Advanced

Consider a star of mass $ m_2 $ kg revolving in a circular orbit around another star of mass $ m_1 $ kg with $ m_1 \gg m_2 $. 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:
Two satellites P and Q are moving in different circular orbits around the Earth (radius 𝑅). The heights of P and Q from the Earth surface are \(β„Ž_P\) and \(β„Ž_Q\), respectively, where \(β„Ž_P = \frac{𝑅}{3}\). The accelerations of P and Q due to Earth’s gravity are \(𝑔_P\) and \(𝑔_Q\), respectively. If \(\frac{𝑔_P}{𝑔_Q} = \frac{36}{25}\), what is the value of \(β„Ž_Q?\)
Two spherical stars $A$ and $B$ have densities $\rho_A$ and $\rho_B$, respectively $A$ and $B$ have the same radius, and their masses $M_A$ and $M_B$ are related by $M_B=2 M_A$ Due to an interaction process, star $A$ loses some of its mass, so that its radius is halved, while its spherical shape is retained, and its density remains $\rho_A$ The entire mass lost by $A$ is deposited as a thick spherical shell on $B$ with the density of the shell being $\rho_A$ If $v_A$ and $v_B$ are the escape velocities from $A$ and $B$ after the interaction process, the ratio \(\frac{v_B}{v_A}=\sqrt{\frac{10 n}{15^{\frac 13}}}\). The value of $n$ is ___ .

The Ratio of gravity field due to the earth at high hP and hQ from the earth's surface is \(\frac{g_{P}}{g_{Q}}=\frac{36}{25}.\) If \(h_P=\frac{R}{2}\), then the value of hQ will be

Two spherical stars $A$ and $B$ have densities $\rho_A$ and $\rho_B$, respectively $A$ and $B$ have the same radius, and their masses $M_A$ and $M_B$ are related by $M_B=2 M_A$ Due to an interaction process, star $A$ loses some of its mass, so that its radius is halved, while its spherical shape is retained, and its density remains $\rho_A$ The entire mass lost by $A$ is deposited as a thick spherical shell on $B$ with the density of the shell being $\rho_A$ If $v_A$ and $v_B$ are the escape velocities from $A$ and $B$ after the interaction process, the ratio $\frac{v_B}{v_A}=\sqrt{\frac{10 n}{15^{1 / 3}}}$ The value of $n$ is ___

The distance between two stars of masses 3MS and 6MS is 9R. Here R is the mean distance between the centres of the Earth and the Sun, and MS is the mass of the Sun. The two stars orbit around their common centre of mass in circular orbits with period nT, where T is the period of Earth’s revolution around the Sun. The value of n is ___.
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]
One twirls a circular ring (of mass $M$ and radius $R$ ) near the tip of one's finger as shown in Figure 1. In the process the finger never loses contact with the inner rim of the ring. The finger traces out the surface of a cone, shown by the dotted line. The radius of the path traced out by the point where the ring and the finger is in contact is $r$. The finger rotates with an angular velocity $\omega_{0}$. The rotating ring rolls without slipping on the outside of a smaller circle described by the point where the ring and the finger is in contact (Figure 2). The coefficient of friction between the ring and the finger is $\mu$ and the acceleration due to gravity is $g$. The total kinetic energy of the ring is
A planet of radius $R=\frac{1}{10}$ x (radius of earth) has the same mass density as earth. Scientists dig a well of depth $\frac{R}{5}$ on it and lower a wire of the same length and of linear mass density $10^{-3}$ $kgm^{-1}$ into it. If the wire is not touching anywhere, the force applied at the top of the wire by a person holding it in place is (take the radius of earth = $6 \times 10^6$ m and the acceleration due to gravity of earth is $10 \,ms^{-2}$)
A satellite is moving with a constant speed $v$ in a circular orbit about the earth. An object of mass '$m$' is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of its ejection, the kinetic energy of the object is :
A thin uniform annular disc (see figure) of mass $M$ has outer radius $4R$ and inner radius $3R$. The work required to take a unit mass from point $P$ on its axis to infinity is
A double star system consists of two stars A and B which have time periods $T_ A $ and $T_B $ . Radius $ R_A $ and $ R_B $ and mass $ M_A $ and $M_B $ . Choose the correct option
A geostationary satellite orbits around the earth in a circular orbit of radius $36,000\, km$. Then, the time period of a spy satellite orbiting a few hundred km above the earth's surface $ (R_ e = 6400km) $ will approximately be
A simple pendulum has a time period $T_1$ when on the earth's surface and $T_2 $ when taken to a height R above the earth's surface, (where R is the radius of the earth). The value of $ T_2/T_1 $ is
If the distance between the earth and the sun were half its present value, the number of days in a year would have been
Imagine a light planet revolving around a very massive star in a circular orbit of radius R with a period of revolution T. If the gravitational force of attraction between the planet and the star is proportional to $ R^{-5/2} $ , then
A satellite $S$ is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Then,