Gravitation practice · Medium

The angle between the equatorial plane and the orbital plane of a polar satellite and geostationary satellite are respectively

The orbital velocity of a body close to the earth's surface is

In the above question, if the angular velocity is kept same but the radius of the path is halved, the new force will be

Kepler's law states that, square of the time period of any planet moving around the sun in an elliptical orbit of semi-major axis $(R)$ is directly proportional to

The radii of circular orbits of two satellites A and B of the earth, are 4R and R, respectively if speed of satellite A is 2V, then the speed of satellite B will be

A car is moving with speed 30 m/sec on a circular path of radius 500 m. Its speed is increasing at the rate of $2m/{\sec ^2}$ , What is the acceleration of the car

Centripetal acceleration is

An iron ball and a wooden ball of the same radius are released from a height 'h' in vacuum. The time taken by both of them to reach the ground is

Two spaceships are travelling in the same direction. An astronaut in first ship drops a coin and finds that the coin stays at rest. An astronaut in second ship drops a coin and finds that the coin starts moving in forward direction with an acceleration of $2 \mathrm{~m} / \mathrm{s}^2$. Assume that the coin is uncharged and the whole system is in gravity free space:

A satellite can be in a geostationary orbit around earth in an orbit of radius $r$ . If the angular velocity of earth about its axis doubles, a satellite can now be in a geostationary orbit around earth of radius

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : The escape velocities of planet $A$ and $B$ are same. But $A$ and $B$ are of unequal mass.
Reason R : The product of their mass and radius must be same, ${M_1}{R_1} = \mathrm{ }{M_2}{R_2}$
In the light of the above statements, choose the most appropriate answer from the options given below.

What should be the angular velocity of earth so that a body on its equator is weightless?

The earth revolves about the sun in an elliptical orbit with mean radius $9.3 \times {10^7}m$ in a period of 1 year. Assuming that there are no outside influences

A particle of mass $m$ is dropped from a great height $h$ above the hole in the earth dug along its diameter. Then, which of the following statement is correct?

The acceleration due to gravity increase by $0.5\%$ when we go from the equator to the poles. What will be the time period of the pendulum at the equator which beats seconds at the poles?

If satellite is shifted towards the earth. Then time period of satellite will be

A particle does uniform circular motion in a horizontal plane. The radius of the circle is 20 cm. The centripetal force acting on the particle is 10 N. It's kinetic energy is

Gravitational force between two point masses is found to be F when both are in vacuum. If both the masses are immersed in water, new gravitational force will be

A satellite of the earth is revolving in a circular orbit with a uniform speed $v$. If the gravitational force suddenly disappears, the satellite will

A body of mass m is taken to the boom of a deep mine. Then

Every planet revolves around the sun in an elliptical
orbit:

A. The force acting on a planet is inversely
proportional to square of distance from sun.

B. Force acting on planet is inversely proportional
to product of the masses of the planet and the
sun.

C. The Centripetal force acting on the planet is
directed away from the sun.

D. The square of time period of revolution of
planet around sun is directly proportional to
cube of semi-major axis of elliptical orbit.

Choose the correct answer from the options given
below:

Two satellites of earth, ${S_1}\,and\,{S_2}$, are moving in the same orbit. The mass of ${S_1}$ is four times the mass of ${S_2}$. Which one of the following statements is true?

The maximum and minimum distances of a comet from the sun are $1.4 \times {10^{12}}m\,and\,6 \times {10^{10}}m$ respectively. If its velocity nearest to the sun is $7 \times {10^4}\mathrm{m}{\mathrm{s}^{ - 1}}$, what is the velocity in the farthest position? Assume the paths of comet in both instantaneous positions are circular

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:

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

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

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 $= 1.5 \times {10^{11}}m$ )