Embibe Experts Solutions for Chapter: Gravitation, Exercise 2: Exercise-2

If two spheres of same masses and radius are brought in contact, then the force of attraction between them will be proportional to (for a given density $\rho$)

Assume the earth to be a sphere of radius $R$. If $g$ is the acceleration due to gravity at any point on the earth's surface, the mass of the earth is:

Energy required to transfer a $400 \mathrm{kg}$ satellite in a circular orbit of radius $2R$ to a circular orbit of radius $4R$, where$R$  is the radius of the earth. [Given $g=9.8{ \mathrm{m} \mathrm{s}}^{-2}, R=6.4\times {10}^6 \mathrm{m}$]

A double star system consists of two stars $A$ and $B$ which have time period $T_A$ and $T_B.$ Radius $R_A$ and $R_B$ and mass $M_A$ and $M_B$. Choose the correct option.

Mass $M$ is uniformly distributed only on the curved surface of a thin hemispherical shell. $A, B$ and $C$ are three points on the circular base of the hemisphere, such that $A$ is the centre. Let the gravitational potential at points $A, B$ and $C$ be $V_A,V_B,V_C$ respectively. Then

Assertion: In free space, a uniform spherical planet of mass $M$ has a smooth narrow tunnel along its diameter. This planet and another super-dense small particle of mass $M$ start approaching towards each other from rest under the action of their gravitational forces. When the particle passes through the centre of the planet, the sum of kinetic energies of both the bodies is maximum.

Reason: When the resultant of all forces acting on a particle or a particle like object (initially, at rest) is constant in direction, the kinetic energy of the particle keeps on increasing.

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.