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

Two satellites A and B of masses 200 kg and 400 kg are revolving round the earth at height of 600 km and 1600 km respectively.

If T_A and T_B are the time periods of A and B respectively then the value of T_B $$-$$ T_A :


[Given : radius of earth = 6400 km, mass of earth = 6 $$\times$$ 10²⁴ kg]

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

Reason R : The product of their mass and radius must be same. M₁R₁ = M₂R₂

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

A body weights 49N on a spring balance at the north pole. What will be its weight recorded on the same weighing machine, if it is shifted to the equator?

[Use $$g = {{GM} \over {{R^2}}}$$ = 9.8 ms^$$-$$2 and radius of earth, R = 6400 km.]