The planet Mars has two moons, if one of them has a period 7 hours, 30 minutes and an orbital radius of 9.0 $$\times$$ 10³ km. Find the mass of Mars.

$$\left\{ {Given\,{{4{\pi ^2}} \over G} = 6 \times {{10}^{11}}{N^{ - 1}}{m^{ - 2}}k{g^2}} \right\}$$

A particle of mass M originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation

$$F = {F_0}\left[ {1 - {{\left( {{{t - T} \over T}} \right)}^2}} \right]$$

Where F₀ and T are constants. The force acts only for the time interval 2T. The velocity v of the particle after time 2T is :

The resistance of a conductor at 15$$^\circ$$C is 16$$\Omega$$ and at 100$$^\circ$$C is 20$$\Omega$$. What will be the temperature coefficient of resistance of the conductor?

In the given figure, two wheels P and Q are connected by a belt B. The radius of P is three times as that of Q. In case of same rotational kinetic energy, the ratio of rotational inertias $$\left( {{{{I_1}} \over {{I_2}}}} \right)$$ will be x : 1. The value of x will be _____________.