Gravitation

Which of the following graphs between the square of the time period and cube of the distance of the planet from the sun is correct?

The escape velocity of a body depends upon mass as (m → mass of projected body)

Legend has it that observing an apple falling from a tree, .... A.... was inspired to arrive at an .... B.... that led to an explanation of .... C.... as well as of .... D.... Here, $A,B,C$ and $D$ refer to

What will be the formula of mass of the earth in terms of g and R? (g = acceleration due to gravity near earth surface, $R=$ Radius of earth)

A particle of mass $m$ is thrown upwards from the surface of the earth, with a velocity $u$. The mass and the radius of the earth are, respectively, $M$ and $R.G$ is gravitational constant and $g$ is acceleration due to gravity on the surface of the earth. The minimum value of $u$ so that the particle does not return back to earth, is

Which of the following statements is correct regarding the universal gravitational constant?

Kepler's law of orbit was a deviation from the

A body weighs 250 N on the surface of the earth. How much will it weigh half way down to the centre of the earth?

A body has a weight 72 N . When it is taken to a height $h=R=$ radius of earth, it would weigh

If $v_{e}$ is escape velocity and $v_{o}$ is orbital velocity of a satellite for orbit close to the earth's surface. Then these are related by

The radii of circular orbits of two satellites A and B of the earth, are 4R and R, respectively. If the speed of satellite A is 3 V , then the speed of satellite B will be:

Which of the following statements is correct?

Two planets A and B have densities ' $\rho_{1}{ }^{\prime},{ }^{\prime} \rho_{2}{ }^{\prime}$ and have radii ' $r_{1}{ }^{\prime},{ }^{\prime} r_{2}{ }^{\prime}$, respectively. The ratio of acceleration due to gravity on $A$ to that of $B$ is

A planet moving along an elliptical orbit is closest to the sun at a distance of $r_{1}$ and farthest away at a distance of $r_{2}$. If $v_{1}$ and $v_{2}$ are the linear velocities at these points respectively, then the ratio $\dfrac{v_{1}}{v_{2}}$ is

Which of the following statements is correct regarding the gravitational force?