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

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

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):

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 $\left(\frac{R}{2}\right)$ <!-- [if gte mso 9]><xml> </xml><![endif]--> is made in the sphere (as shown in figure) and the force becomes F₂. The value of F₁: F₂ is: