Gravitation

The height at which the weight of an object becomes (1/16)^th of its weight on the surface of earth is (R is radius of earth)

In the equation of angular displacement of a particle moving on a circular path is given as is in radian and t in second. Theq angular velocity of the particle at t = 2 s is

If an object is having same weight at same distance above and below the surface of earth, find its distance from surface of earth.

Two bodies of mass $\mathrm{m}$ and $9\mathrm{m}$ are placed at a distance $\mathrm{R}$ . The gravitational potential on the line joining the bodies where the gravitational field equals zero, will be ( $\mathrm{G}=$  gravitational constant):

On the $$ $x$ -axis and at a distance $x$ $$ from the origin, the gravitational field due to a mass distribution is given by $\frac{Ax}{{\left(x^2+a^2\right)}^{3/2}}$ $\frac{}{{\left({}^{}{}^{}\right)}^{}}$ in the $x$ $$ -direction. The magnitude of gravitational potential on the $x$ $$ -axis at a distance $x$ $$ , taking its value to be zero at infinity is:

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 Ad and B are same. But A and B are of unequal mass.

Reason R : The product of their mass and radius must be same. M₁ R₁ = M₂R₂

In the light of the above statements, choose the most appropriate answer from the options given below:

A solid sphere of radius R gravitationally attracts a particle placed at 3R form its centre with a force F₁,. Now a spherical cavity of radius $\left(\frac{R}{2}\right)$  is made in the sphere (as shown in figure) and the force becomes F₂. The value of F₁: F₂ is:

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 $2R$  from the surface of the earth is:

A parallel plate capacitor is charged by connecting it to a battery through a resistor. If $I$  is the current in the circuit, then in the gap between the plates:

The satellites revolve around a planet in coplanar circular orbits in anticlockwise direction. Their period of revolutions are 1 hour and 8 hour respectively. The radius of the orbit of nearer satellite is 2 * 10³ km. The angular speed of the farther satellite as observed from the nearer satellite at the instant when both the satellites are closest is $\frac{\pi }{x}rad{h}^{-1}$ where x is__________.