Embibe Experts Solutions for Chapter: Gravitation, Exercise 1: Exercise 1

A planet has a mass $M_1$ and radius $R_1$. The value of acceleration due to gravity on its surface is $g_1$. There is another planet $2$, whose mass and radius both are two times that of the first planet. Which one of the following is the acceleration due to gravity on the surface of planet $2$?

Imagine a new planet having the same density as that of the earth but it is $3$ times bigger than the earth in size. If the acceleration due to gravity on the surface of the earth is $g$ and on the surface of the new planet is $g^{\text{'}}$, then

Assertion: If the earth suddenly stops rotating about its axis, then the value of effective acceleration due to gravity $\left(g_{\mathrm{effective}}\right)$ will become the same at all the places. (Assume earth to be spherical)

Reason: The value of effective acceleration due to gravity $\left(g_{\mathrm{effective}}\right)$ is independent of the rotation of the earth.

Assertion: Gravitational potential of the earth at every place on its is negative. (taking potential at infinity to be zero)

Reason: Everybody on earth is bound by the attraction of earth.

An object is propelled vertically to a maximum height of $4R$ from the surface of a planet of radius $R$ and mass $M.$ The speed of the object when it returns to the surface of the planet is

A planet revolves about the sun in elliptical orbit. The areal velocity $\left(\frac{\mathrm{d}A}{\mathrm{d}t}\right)$ of the planet is $4.0\times {10}^{16} {\mathrm{m}}^2 {\mathrm{s}}^{-1}$. The least distance between planet and the sun is $2\times 10^{12} \mathrm{m}$. Then the maximum speed of the planet in $\mathrm{km} {\mathrm{s}}^{-1}$ is-

The time period of an earth satellite in circular orbit is independent of

A cosmonaut is orbiting earth in a spacecraft at an altitude $h=630 \mathrm{km}$ with a speed of $8 \mathrm{km} {\mathrm{s}}^{-1}$. If the radius of the earth is $6400 \mathrm{km}$, the acceleration of the cosmonaut is