List of top Physics Questions on Gravitation asked in JEE Main

Suppose two planets (spherical in shape) of radii R and 2 R, but mass M and 9 M respectively have a centre to centre separation 8 R as shown in the figure. A satellite of mass 'm' is projected from the surface of the planet of mass 'M' directly towards the centre of the second planet. The minimum speed 'v' required for the satellite to reach the surface of the second planet is $\sqrt{\frac{aGM}{7R}}$ then the value of 'a' is _________. [Given : The two planets are fixed in their position] 

 

Two satellites A and B of masses 200 kg and 400 kg are revolving round the earth at height of 600 km and 1600 km respectively. If $T_A$ and $T_B$ are the time periods of A and B respectively then the value of $T_B - T_A$ is : [$R_e = 6400$ km, $M_e = 6 \times 10^{24}$ kg]
 

A solid sphere of radius R gravitationally attracts a particle placed at 3R from its centre with a force $F_1$. Now a spherical cavity of radius (R/2) is made in the sphere (as shown in figure) and the force becomes $F_2$. The value of $F_1 : F_2$ is :

Two stars of masses $m$ and $2m$ at a distance $d$ rotate about their common centre of mass in free space. The period of revolution is :
Four identical particles of equal masses 1 kg made to move along the circumference of a circle of radius 1 m under the action of their own mutual gravitational attraction. The speed of each particle will be :
Consider two satellites $S_1$ and $S_2$ with periods of revolution 1 hr. and 8 hr. respectively revolving around a planet in circular orbits. The ratio of angular velocity of satellite $S_1$ to the angular velocity of satellite $S_2$ is :

A particle of mass \(m\) moves in a circular orbit under the central potential field, \(U(r) = -\frac{C}{r}\), where \(C\) is a positive constant. The correct radius – velocity graph of the particle's motion is: 

If the angular velocity of earth's spin is increased such that the bodies at the equator start floating, the duration of the day would be approximately: [Take \(g = 10\) ms⁻², \(R = 6400 \times 10^3\) m, \(\pi = 3.14\)]
The angular momentum of a planet of mass \(M\) moving around the sun in an elliptical orbit is \(\vec{L}\). The magnitude of the areal velocity of the planet is:
The planet Mars has two moons, if one of them has a period 7 hours, 30 minutes and an orbital radius of $9.0 \times 10^3$ km. Find the mass of Mars.
$\left\{ \text{Given } \frac{4\pi^2}{G} = 6 \times 10^{11} \text{ N}^{-1} \text{ m}^{-2} \text{ kg}^2 \right\}$
Two identical particles of mass 1 kg each go round a circle of radius R under the action of their mutual gravitational attraction. The angular speed of each particle is :
Planet $A$ has mass $M$ and radius $R$. Planet $B$ has half the mass and half the radius of Planet $A$. If the escape velocities from the Planets $A$ and $B$ are $v_A$ and $v_B$, respectively, then $\frac{v_{A}}{v_{B}}=\frac{n}{4}$. The value of $n$ is :
Consider two solid spheres of radii $R, = 1m, \,R_2 = 2m$ and masses $M_1$ and $M_2$, respectively. The gravitational field due to sphere (1) and (2) are shown. The value of $\frac{m_{1}}{m_{2}}$ is :
Shown in the figure is a hollow icecream cone (it is open at the top). If its mass is $M ,$ radius of its top, $R$ and height, $H ,$ then its moment of inertia about its axis is: 
A straight rod of length $L$ extends from $x = a$ to $x = L + a$. The gravitational force is exerts on a point mass $'m'$ at $x = 0$, if the mass per unit length of the rod is $A + Bx^2$, is given by:
A test particle is moving in a circular orbit in the gravitational field produced by a mass density \(\rho(r) = \frac{K}{r^2}\). Identify the correct relation between the radius \(R\) of the particle's orbit and it's period \(T\) :
A solid sphere of mass $'M'$ and radius $'a'$ is surrounded by a uniform concentric spherical shell of thickness $2a$ and mass $2M$. The gravitational field at distance $'3a'$ from the centre will be :
A satellite of mass $M$ is in a circular orbit of radius $R$ about the centre of the earth. A meteorite of the same mass, falling towards the earth, collides with the satellite completely inelastically. The speeds of the satellite and the meteorite are the same, just before the collision. The subsequent motion of the combined body will be :
Four identical particles of mass $M$ are located at the corners of a square of side $'a'$. What should be their speed if each of them revolves under the influence of other?s gravitational field in a circular orbit circumscribing the square?
If the angular momentum of a planet of mass $m$, moving around the Sun in a circular orbit is $L$, about the center of the Sun, its areal velocity is :
A particle is moving with a uniform speed in a circular orbit of radius $R $ in a central force inversely proportional to the nth power of $R$. If the period of rotation of the particle is $T$ then -
The variation of acceleration due to gravity $g$ with distance $d$ from centre of the earth is best represented by (R = Earth?s radius) :
A satellite is revolving in a circular orbit at a height ' $h$' from the earth's surface (radius of earth $R ; h < < R$). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth?s gravitational field, is close to : (Neglect the effect of atmosphere.)
Figure shows elliptical path abcd of a planet around the sun $S$ such that the area of triangle $csa$ is $\frac{1}{4}$ the area of the ellipse. (See figure) With $db$ as the $semimajor$ axis, and $ca$ as the $semiminor$ axis. If $t_1$ is the time taken for planet to go over path $abc$ and $t_2$ for path taken over $cda$ then :
A very long (length L) cylindrical galaxy is made of uniformly distributed mass and has radius $R (R << L)$. A star outside the galaxy is orbiting the galaxy in a plane perpendicular to the galaxy and passing through its centre. If the time period of star is $T$ and its distance from the galaxy's axis is $r$, then :