The initial pressure and volume of an ideal gas are P$$_0$$ and V$$_0$$. The final pressure of the gas when the gas is suddenly compressed to volume $$\frac{V_0}{4}$$ will be :

(Given $$\gamma$$ = ratio of specific heats at constant pressure and at constant volume)

Given below are two statements: one is labelled as Assertion $$\mathbf{A}$$ and the other is labelled as Reason $$\mathbf{R}$$

Assertion A : A spherical body of radius $$(5 \pm 0.1) \mathrm{mm}$$ having a particular density is falling through a liquid of constant density. The percentage error in the calculation of its terminal velocity is $$4 \%$$.

Reason R : The terminal velocity of the spherical body falling through the liquid is inversely proportional to its radius.

In the light of the above statements, choose the correct answer from the options given below

A vehicle of mass $$200 \mathrm{~kg}$$ is moving along a levelled curved road of radius $$70 \mathrm{~m}$$ with angular velocity of $$0.2 ~\mathrm{rad} / \mathrm{s}$$. The centripetal force acting on the vehicle is:

Two planets A and B of radii $$\mathrm{R}$$ and 1.5 R have densities $$\rho$$ and $$\rho / 2$$ respectively. The ratio of acceleration due to gravity at the surface of $$\mathrm{B}$$ to $$\mathrm{A}$$ is: