Physics

Why is pressure proportional to the square of molecular speed in an ideal gas?

Shown in the figure is rigid and uniform one meter long rod AB held in horizontal position by two strings tied to its ends and attached to the ceiling. The rod is of mass 'm' and has another weight of mass 2m hung at a distance of 75 cm from A. The tension in the string at A is:

Train A and train B are running on parallel tracks in opposite directions with speed of 36 km/hour and 72 km/hour, respectively. A person is walking in train A in the direction opposite to its motion with a speed of 1.8 km/hour. Speed (in ms⁻¹) of this person as observed from train B will be close to: (take the distance between the tracks as negligible)

In a reactor, 2 kg of ₉₂U²³⁵ fuel is fully used up in 30 days. The energy released per fission is 200MeV. Given that the Avogadro number, N = 6.023 * 10²⁶ per kilo mole and 1eV = 1.6 * 10⁻¹⁹ J. The power output of the reactor is close to:
(A) 60MW

A beam of protons with speed 4 * 10⁵ ms⁻¹ enters a uniform magnetic field of 0.3 T at an angle of 60° to the magnetic field. The pitch of the resulting helical path of protons is close to: (Mass of the proton = 1.67 * 10⁻²⁷ kg, charge of the proton = 1.69 * 10⁻¹⁹ C)

A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T. Assuming the gases to be ideal and the oxygen bond to be rigid, the total internal energy (in units of RT) of the mixture is:

An amplitude modulated wave is represented by the expression vₘ = 5(1 + 0.6cos 6280t)sin(211 * 10⁴t) volts. The minimum and maximum amplitudes modulated wave are respectively

A small block starts slipping down from a point B on an inclined plane AB, which is making an angle θ with the horizontal section BC. Section BC is smooth and the remaining section CA is rough with a coefficient of friction µ. It is found that the block comes to rest as it reaches the bottom (point A) of the inclined plane. If BC = 2AC, the coefficient of friction is given by µ = k tanθ. The value of k is

If speed V, area A and force F are chosen as fundamental units, then the dimension of Young's modulus will be

A 5µF capacitor is charged fully by a 220 V supply. It is then disconnected from the supply and is connected in series to another uncharged 2.5µF capacitor. If the energy change during the charge redistribution is X/100 J then value of X to the nearest integer is: