A galvanometer, whose resistance is 50 ohm, has 25 divisions in it. When a current of 4 $$ \times $$ 10^–4 A passes through it, its needle ( pointer) deflects by one division. To use this galvanometer as a voltmeter of range 2.5 V, it should be connected to a resistance of :

A particle of mass 20 g is released with an initial velocity 5 m/s along the curve from the point A, as shown in the figure. The point A is at height h from point B. The particle slides along the frictionless surface. when the particle reaches point b, its angular momentum about O will be :
(Take g = 10 m/s²)

An ideal gas is enclosed in a cylinder at pressure of 2 atm and temperature 300 K. The mean time between two successive collisions is 6 $$ \times $$ 10^–8 s. If the pressure is doubled and temperature is increased to 500 K, the mean time between two successive collisions will be close to

In the circuit shown, find C if the effective capacitance of the whole circuit is to be 0.5 $$\mu $$F. All values in the circuit are in $$\mu $$F.