Supposing Newton's law of gravitation for gravitation forces F₁ and F₂ between two masses m₁ and m₂ at positions r₁ and r₂ read F₁=-F₂=- $\frac{{\mathit{r}}_{12}}{{\mathit{r}}_{12}^3}\mathit{G}{\mathit{M}}_{\mathit{o}}^2\left(\frac{{\mathit{m}}_1{\mathit{m}}_2}{{\mathit{M}}_{\mathit{o}}^2}\right)$ ⁿ where M_o is a constant of dimension of mass, r₁₂ = r₁ – r₂ and n is a number. In such a case,

(a) The acceleration due to gravity on earth will be different for different objects.

(b) None of the three laws of Kepler will be valid.

(c) Only the third law will become invalid.

(d) For n negative, an object lighter than water will sink in water.

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):

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: