Gravitation practice · Mixed difficulty

If the gravitational acceleration at the surface of earth is g, then increase in potential energy in lifting an object of mass m from earth surface to a height equal to half of radius of earth from surface will be:

Mars has a diameter of approximately 0.5 of that of Earth and mass of 0.1 of that of Earth. The surface gravitational field strength on Mars as compared to that on Earth is greater by a factor of

Kepler’s second law regarding constancy of aerial velocity of a planet is consequence of the law of conservation of

Given below are two statements: One is labelled as
Assertion A and the other is labelled as Reason R.

Assertion A: A pendulum clock when taken to
Mount Everest becomes fast.

Reason R: The value of $g$ (acceleration due to
gravity) is less at Mount Everest than its value on the
surface of earth.

In the light of the above statements, choose the
most appropriate answer from the options given
below

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

Two identical satellites are at $R$ and $7R$ away from earth surface, the wrong statement 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

Assertion: Gravitational force between two particles is negligibly small compared to the electrical force.
Reason: The electrical force is experienced by charged particles only.

Both earth and moon are subject to the gravitational force of the sun. As observed from the sun, the orbit of the moon

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

The planet Saturn revolves around the sun with a time period of 27 years. The ratio of orbital radii of Saturn to that of earth is (orbital radius of earth $= 1.5 \times {10^{11}}m$ )

Determine the energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 3R.

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

Assertion: If value of acceleration due to gravity of a planet is lesser than earth then escape velocity from planet is lesser too.
Reason: Escape velocity just depends only on acceleration due to gravity.

A rectangular plank of mass ${m_1}$ and height a is kept on a horizontal surface. Another rectangular plank of mass ${m_2}$ and height b is placed over the first plank. The gravitational potential energy of the system is

Average density of the earth

A particle of mass m is moving in a horizontal circle of radius r,under a centripetal force $= \frac{k}{{{r^2}'}}\;\mathrm{where\;}k\mathrm{\;is\;a\;constant}.$

Where will it be profitable to purchase 1 kilogram sugar

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 radius of earth is 6400 km. At what depth below the surface of earth the acceleration due to gravity decreases by 2% than on surface of earth.

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%.

Assertion: If gravitational force is proportional to $\frac{1}{\mathrm{R}^3}$ then Keplar's second law would not be affected.
Reason: For Keplar's second law, central nature of force is the only condition.

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

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

If the earth rotates faster than its present speed, the weight of an object will

The weight of the body at the centre of the earth is