Gravitation practice · Easy

The value of ‘g’ at a particular point on the surface of the earth is $9.8\,m{s^{ - 2}}.$ Suppose the earth suddenly shrinks uniformly to ${\frac{1}{4}^{th}}$ of its present size without losing mass, then the value of ‘g’ on the surface of new earth will be

The force of gravitation is

Statement-1: In elliptical orbit around the sun, the earth is closer to the sun during summer than during winter.
Statement-2: The angular momentum of the earth about the sun is not conserved.

Statement-1: The speed of satellite always remains constant in an orbit
Statement-2: The speed of a satellite depends on its path.

Statement-1: Two particles are to be projected from the surface of earth so that particles just leave the gravitational field of earth. One particle is projected vertically upward and another is at an angle of $45^{\circ}$ with vertical. Speed given to both particles is same.
Statement-2: Escape speed does not depend upon angle of projection.

A satellite is moving in a circular orbit round the earth with a diameter of orbit $2 R$. At a certain point a rocket fixed to the satellite is fired such that it increases the velocity of the satellite tangentially. The resulting orbit of the satellite would be

A body revolved around the sun 27 times faster than the earth. What is the ratio of their radii

A person can jump safely from a height of 8 m on the earth on a planet where acceleration due to gravity is $5\,m{s^{ - 2}},$ the maximum height from which can jump safely $\left[ {{g_e} = 10\,m{s^{ - 2}}} \right]$

Statement-1: A particle is at a height ${R}$ from the surface of earth (Here ${R}$ is radius of earth). If mass of particle is ${m}$ then its gravitational potential energy is ${mgR}$
Statement-2: If a particle is slowly lifted above the surface of earth then work is done by external agent. Work done by external agent is wasted in the form of heat energy.

Statement-1: Work done by gravitational field in cyclic process is zero
Statement-2: Work done by conservative field does not depend upon path.

Statement-1: A planet is moving around the sun in an elliptical orbit. Then from aphelion point to perihelion point the speed of the planet continuously increases.
Statement-2: According to Kepler's second law, the areal velocity of the line joining planet to the sun is constant.

Assertion: The change of weight with height $h$ near the earth's surface is proportional to $h^0$
Reason: Since gravitational potential is given by $V=-G M / r$

The percentage decrease in the weight of a rocket, when taken to a height of $32 \mathrm{~km}$ above the surface of earth will, be:

(Radius of earth $=6400 \mathrm{~km}$ )

Assertion(A): If radius of earth suddenly shrinks to half its present value without changing its mass, then the period of an earth's satellite will not change.
Reason(R): Time period of a satellite does not depend upon the mass of earth.

Period of revolution of a geostationary satellite around the earth is

Assume that the earth rotates in a circular orbit round the sun in 365 days. If the mass of the sun gets four time but the radius of the orbit remains unchanged, the length of the year would be approximately.

A satellite is moving around the earth with speed V in a circular orbit of radius r. If the orbit radius is decreased by 1%, its speed will

Infinite number of masses each 2 kg are placed along the x-axis at $x = \pm 1\,m,\, \pm 2\,m,\, \pm \,4\,m,\, + ......$ The magnitude of the resultant gravitational potential in terms of gravitation constant G at the origin (x = 0) is

The ratio of the accelerations due to gravity on two planets $P_1 \& P_2$ is $K_1$. The ratio of their respective radii is $K_2$. The ratio of their respective escape velocities is

Masses 2 kg and 18 kg are 12 cm a part. The point along the line joining the masses where the gravitational field due to them is zero is

Gravitational potential energy of a body of mass $m$ at a height of $h$ above the surface of earth $(M=$ mass of earth $R=$ radius of earth) is

On which quantity the escape velocity for earth does not depend on

Statement-1: If earth suddenly stops rotating about its axis then the acceleration due to gravity will become same at all the places.
Statement-2: The value of acceleration due to gravity except at poles is independent of rotation of earth

A body is projected from earth's surface to become its satellite, its time period of revolution will not depend upon

When you move from equator to pole, the value of acceleration due to gravity ( $\mathrm{g}$ )

A small satellite is revolving near earth's surface. Its orbital velocity will be nearly

The diameter of a planet is four times that of the earth. Find the time period of pendulum on the planet, if it is a second pendulum on the earth. Take the mean density of the planet equal to that of the earth.

At which depth from Earth surface, acceleration due to gravity is decreased by 1%.

Statement-1: When a body is projected with velocity $\mathrm{v}=\mathrm{v}_0$ (where $\mathrm{v}_0$ is orbital velocity) then path of the projectile is circular.
Statement-2: Gravitational force between body and the earth provides the centripetal force.

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