Gravitation practice · Mixed difficulty

Assertion: The time period of a pendulum, on a satellite orbiting the earth is infinity.
Reason: Time period of a pendulum is inversly proportional to $\sqrt{g}$

To what height the body is to be raised so that acceleration due to gravity on it is 1% of the value on the surface of earth? (Radius of earth is 6400km)

When earth moves around the sun, the quantity which remains constant is

Statement-1: The gravitational field intensity on the surface of the sphere is $E=\frac{G M}{R^2}$
Statement-2: The gravitational potential on the surface of the sphere is $V=\frac{-G M}{R}$.

The weight of an object in the coal mine, sea level, at the top of the mountain are ${W_1},\;{W_2}\,and\,{W_3}$ respectively, then

The mass of a space ship is 500 kg. It is to be launched from the earth’s surface out into free space. The value of ‘$g$’ and ‘$R$’ (radius of earth) are $10\,m{s^{ - 2}}$ and 6400 km respectively. The required energy for this work will be [in Joules]

A body of mass $m$ is taken from earth surface to the height $\mathrm{h}$ equal to radius of earth, the increase in potential energy will be

Statement-1: The force of attraction due to a hollow spherical shell of uniform density, on a point mass situated inside it is zero.
Statement-2: The gravitation field due to the shell inside the shell will be zero.

A double star system consists of two stars A and B which have time period ${T_A}\;\mathrm{and\;}{\mathrm{T}_\mathrm{B}}$. Radius ${R_A}\;\mathrm{and\;}{R_B}$ and mass ${M_A}\;\mathrm{and\;}{M_B}$. Choose the correct option.

Compute the additional velocity required by a satellite orbiting around earth with radius $2 R$ to become free from earth's gravitational field. Mass of earth is $M$.

A person sitting on a chair in a satellite feels weightless because

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

Assertion: Work done by or against gravitational force in moving a body from one point to another is independent of the actual path followed between the two points.
Reason: Gravitational forces are conservative forces.

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

An astronaut floating weightlessly in space shakes a large iron block rapidly back and forth. She compares that to her moving it on earth on a smooth horizontal surface. She find that:

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

If the gravitational force between two objects were proportional to $1 / R$ (and not as $1 / R^2$ ) where $R$ is separation between them, then a particle in circular orbit under such a force would have its orbital speed $v$ 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

Statement-1: The angular momentum under a central force is constant.
Statement-2: A force directed towards a fixed point following inverse square law is conservative

When we move from equator to pole, the value of acceleration due to gravity(g)

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

Two planets $A$ and $B$ having masses $m_1$ and $m_2$ move around the sun in circular orbits of $r_1$ and $r_2$ radii respectively. If angular momentum of $\mathrm{A}$ is ${L}$ and that of $B$ is $3 L$, the ratio of time period $\left(\frac{T_A}{T_B}\right)$ is:

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

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.

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:

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