Gravitation practice · Mixed difficulty

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.

The minimum energy required to launch a satellite of mass $m$ from the surface of earth of mass $M$ and radius $R$ in a circular orbit at an altitude of $2 R$ from the surface of the earth is:

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.

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 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.

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?

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 $V=-G M / r$

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

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 $=6400 \mathrm{~km}$ )

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

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.

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?

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.

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

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