Given below are two statements: Statement I: Acceleration due to gravity is different at different places on the surface of earth. Statement II: Acceleration due to gravity increases as we go down below the earth's surface. In the light of the above statements, choose the correct answer from the options given below

At a certain depth "d " below surface of earth, value of acceleration due to gravity becomes four times that of its value at a height $$3R$$ above earth surface. Where $$\mathrm{R}$$ is Radius of earth (Take $$\mathrm{R}=6400\mathrm{km}$$ ). The depth $$\mathrm{d}$$ is equal to

An object is allowed to fall from a height $R$ above the earth, where $R$ is the radius of earth. Its velocity when it strikes the earth's surface, ignoring air resistance, will be

If the gravitational field in the space is given as $$\left(-\frac{K}{r^2}\right)$$. Taking the reference point to be at $$\mathrm{r}=2\mathrm{cm}$$ with gravitational potential $$\mathrm{V}=10\mathrm{J}/\mathrm{kg}$$. Find the gravitational potential at $$\mathrm{r}=3\mathrm{cm}$$ in SI unit (Given, that $$\mathrm{K}=6\mathrm{Jcm}/\mathrm{kg}$$)

The time period of a satellite of earth is 24 hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value, then its new time period will become.

Two particles of equal mass '$$m$$' move in a circle of radius '$$r$$' under the action of their mutual gravitational attraction. The speed of each particle will be :

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 :

A body of mass is taken from earth surface to the height h equal to twice the radius of earth (R$${}_e$$), the increase in potential energy will be : (g = acceleration due to gravity on the surface of Earth)

Assume that the earth is a solid sphere of uniform density and a tunnel is dug along its diameter throughout the earth. It is found that when a particle is released in this tunnel, it executes a simple harmonic motion. The mass of the particle is 100 g. The time period of the motion of the particle will be (approximately) (Take g = 10 m s$${}^{-2}$$ , radius of earth = 6400 km)

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

If the distance of the earth from Sun is 1.5 $$\times$$ 10$${}^6$$ km. Then the distance of an imaginary planet from Sun, if its period of revolution is 2.83 years is :

Given below are two statements: Statement I : Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface. Statement II : Acceleration due to earth's gravity is same at a height 'h' and depth 'd' from earth's surface, if h = d. In the light of above statements, choose the most appropriate answer from the options given below

The weight of a body at the surface of earth is 18 N. The weight of the body at an altitude of 3200 km above the earth's surface is (given, radius of earth $${\mathrm{R}}_{\mathrm{e}}=6400\mathrm{km}$$) :

Two identical particles each of mass ' $m$ ' go round a circle of radius $a$ under the action of their mutual gravitational attraction. The angular speed of each particle will be :

A body is released from a height equal to the radius $(\mathrm{R})$ of the earth. The velocity of the body when it strikes the surface of the earth will be (Given $g=$ acceleration due to gravity on the earth.)

Given below are two statements: Statement I : For a planet, if the ratio of mass of the planet to its radius increases, the escape velocity from the planet also increases. Statement II : Escape velocity is independent of the radius of the planet. In the light of above statements, choose the most appropriate answer form the options given below

Two planets A and B of radii $$\mathrm{R}$$ and 1.5 R have densities $$\rho$$ and $$\rho /2$$ respectively. The ratio of acceleration due to gravity at the surface of $$\mathrm{B}$$ to $$\mathrm{A}$$ is:

A planet having mass $$9\mathrm{Me}$$ and radius $$4{\mathrm{R}}_{\mathrm{e}}$$, where $$\mathrm{Me}$$ and $$\mathrm{Re}$$ are mass and radius of earth respectively, has escape velocity in $$\mathrm{km}/\mathrm{s}$$ given by: (Given escape velocity on earth $${\mathrm{V}}_{\mathrm{e}}=11.2\times 10^3\mathrm{m}/\mathrm{s}$$ )

The ratio of escape velocity of a planet to the escape velocity of earth will be:- Given: Mass of the planet is 16 times mass of earth and radius of the planet is 4 times the radius of earth.

Two satellites $$\mathrm{A}$$ and $$\mathrm{B}$$ move round the earth in the same orbit. The mass of $$\mathrm{A}$$ is twice the mass of $$\mathrm{B}$$. The quantity which is same for the two satellites will be