Gravitation practice · Medium

Two types of balances, the beam balance and the spring balance are commonly used for measuring weight in shops. If we are on the moon, we can continue to use

Statement I: Earth continuously attracts the moon towards its centre and yet the moon does not move towards the centre of earth.

Statement II: The gravitational force of atteraction between the moon and earth provides the necessary centripetal force.

A body of mass $m$ is moving in a circular orbit of radius $R$ about a planet of mass $M$. At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius $\frac{R}{2}$. and the other mass, in a circular orbit of radius $\frac{3 R}{2}$. The difference between the final and initial total energies is :

The orbital speed of Jupiter is

One can easily “weight the earth” by calculating the mass of earth using the formula (in usual notation)

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

Out of the following, the only correct statement about satellites is

Assertion: Angular speed of a planet around the sun increases, when it is closer to the sun.

Reason: Total angular momentum of the system remains constant.

Given below are two statements:

Statement I: If $E$ be the total energy of a satellite moving around the earth, then its potential energy will be $\frac{E}{2}$.

Statement II: The kinetic energy of a satellite revolving in an orbit is equal to the half the magnitude of total energy $E$.


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

A satellite is placed in a circular orbit around earth at such a height that it always remains stationary with respect to earth surface. In such case, its height from the earth surface is

According to Kepler, the period of revolution of a planet ($T$) and its mean distance from the sun ($r$) are related by the equation

An artificial satellite is going round the earth, close to its surface. What is the time taken by it to complete one round? Given radius of the earth $=6400 \mathrm{~km}$.

The mass and radius of the sun are $1.99 \times {10^{30}}kg$ and $R = 6.96 \times {10^8}m$ The escape velocity of a rocket from the sun is

Two spheres of masses $m$ and $2 m$ are separated by distance $d$. A particle of mass $\frac{m}{5}$ is projected straight from $2 m$ towards $m$ with a velocity $v_0$. Which of the following statements is correct?

There is a mine of depth about 2.0 km. In this mine the conditions as compared to those at the surface are

If the distance between the earth and the sun becomes half its present value, the number of days in a year would have been

Radius of the earth is $\mathrm{R}$. If a body is taken to a height $\mathrm{3R}$ from the surface of the earth than change in potential energy will be :-

To have an Earth synchronous satellite it should be launched at the proper height moving from

Assertion: A geostationary satellite rotate in a direction from west to east.
Reason: At midnight when the sun is directly below, it pulls on an object in the same direction as the pull of the earth on that object. At noon when the sun is directly above, its pulls on an object in a direction opposite to the pull of the earth.

If the earth were to spin faster, acceleration due to gravity at the poles

According to Kelper’s law of planetary motion if T represent time period and $r$ is orbital radius, then for two planets these are related as

Assertion: Two blocks of masses $m_1$ and $m_2$ are at rest. They are moving towards each other under the mutual internal force. The velocity of centre of mass is zero.

Reason: There is no effect of external forces on the motion of centre of mass.

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

If the radius of earth’s orbit is made $\frac{1}{4}$th ,then duration of an year will become

If the radius of the earth is 6400 KM. The height above the surface of the earth where the value of acceleration due to gravity will be 1% of its value on the surface of the earth is

Assertion: Kepler's law of areas is equivalent to the law of conservation of angular momentum.
Reason: For planetary motion $\frac{{dA}}{2 \mathrm{~m}}=\frac{{L}}{2 \mathrm{~m}}=$ constant.

If the universal gravitational constant decreases uniformly with time, then the path of earth around sun will be

How much below the surface of the earth does the acceleration due to gravity become $1 \%$ of its value at the earth's surface? Radius of the earth $=6400 \mathrm{~km}$.

Two bodies of masses 2kg and 8kg are separated by a distance of 9 m. the point where the resultant gravitational field intensity is zero is at a distance of

Satellites orbiting the earth have finite life and sometimes debris of satellites fall to the earth. This is because