A projectile is fired from the surface of the earth with a velocity of $5 ms^{-1}$ and angle $\theta$ with the horizontal. Another projectile fired from another planet with a velocity of $3 ms^{-1}$ at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (given, $g = 9.8$ m/s$^2$)

A balloon with mass $m$ is descending down with an acceleration $a$ (where $a < g$). How much mass should be removed from it so that it starts moving up with an acceleration $a$?

A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would Earth (mass = $5.98 \times 10^{24}$ kg) have to be compressed to be a black hole?

Dependence of intensity of gravitational field (E) of Earth with distance (r) from the center of Earth is correctly represented by

Kepler’s third law states that square of period of revolution $(T)$ of a planet around the sun, is proportional to third power of average distance $r$ between sun and planet, that is, $T^2 = K r^3,$ here $K$ is constant.$$If the masses of sun and planet are $M$ and $m,$ respectively then as per Newton’s law of gravitation force of attraction between them is$\\F = \frac{G M m}{r^2},$ here $G$ is gravitational constant.$\\$The relation between $G$ and $K$ is described as

The ratio of escape velocity at earth (vₑ) to the escape velocity at a planet (vₚ) whose radius and mean density are twice as that of earth is

A disc and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?

What is the minimum velocity with which a body of mass $m$ must enter a vertical loop of a radius $R$ so that it can complete the loop?

At what height from the surface of earth the gravitational potential and the value of g are $-5.4 \times 10^7 kg^{-2}$ and $6.0 ms^{-2},$ respectively? (Take the radius of earth as 6400 km.)

The acceleration due to gravity at a height 1 km above the Earth is the same as at a depth $d$ below the surface of Earth. Then $d$ is

The kinetic energies of a planet in an elliptical orbit about the Sun, at positions A, B, and C are $K_A, K_B,$ and $K_C,$ respectively. AC is the major axis and SB is perpendicular to AC at the position of the Sun S. Then

If the mass of the Sun were ten times smaller and the universal gravitational constant were ten times larger in magnitude, which of the following is not correct?

A body weighs $200$ N on the surface of the earth. How much will it weigh half way down to the centre of the earth?

The work done to raise a mass $m$ from the surface of the earth to a height $h,$ which is equal to the radius of the earth, is:

A body weighs $72$ N on the surface of the earth. What is the gravitational force on it, at a height equal to half the radius of the earth?

A particle is released from height $S$ from the surface of the Earth. At a certain height, its kinetic energy is three times its potential energy. The height from the surface of Earth and the speed of the particle at that instant are respectively:

The escape velocity from the Earth's surface is $v.$ The escape velocity from the surface of another planet having a radius four times that of Earth and same mass density is:

A particle of mass $m$ is projected with a velocity $v = k V_e (k < 1)$ from the surface of the Earth.$\newline (V_e =$escape velocity$) \newline$The maximum height above the surface reached by the particle is:

A body of mass $60$ g experiences a gravitational force of $3.0$ N, when placed at a particular point. The magnitude of the gravitational field intensity at that point is:

Two bodies of mass $m$ and $9m$ are placed at a distance $R.$ The gravitational potential on the line joining the bodies where the gravitational field equals zero will be ($G$ = gravitational constant):

A satellite is orbiting just above the surface of the earth with period $T.$ If $d$ is the density of the earth and $G$ is the universal constant of gravitation, the quantity $\frac{3Gd}{\pi}$ represents:

The minimum energy required to launch a satellite of mass $m$ from the surface of earth of mass $M$ and radius $R$ in a circular orbit at an altitude of $2R$ from the surface of the earth is:

The mass of a planet is $\frac{1}{10}$ that of the earth and its diameter is half that of the earth. The acceleration due to gravity on that planet is: