A charge particle moves along circular path in a uniform magnetic field in a cyclotron. The kinetic energy of the charge particle increases to 4 times its initial value. What will be the ratio of new radius to the original radius of circular path of the charge particle :

For a series LCR circuit, I vs $$\omega$$ curve is shown :

(a) To the left of $$\omega$$_r, the circuit is mainly capacitive.

(b) To the left of $$\omega$$_r, the circuit is mainly inductive.

(c) At $$\omega$$_r, impedance of the circuit is equal to the resistance of the circuit.

(d) At $$\omega$$_r, impedance of the circuit is 0.

Choose the most appropriate answer from the options given below :

A block of metal weighing 2 kg is resting on a frictionless plane (as shown in figure). It is struck by a jet releasing water at a rate of 1 kgs^$$-$$1 and at a speed of 10 ms^$$-$$1. Then, the initial acceleration of the block, in ms^$$-$$2, will be :

In van der Waal equation $$\left[ {P + {a \over {{V^2}}}} \right]$$ [V $$-$$ b] = RT; P is pressure, V is volume, R is universal gas constant and T is temperature. The ratio of constants $${a \over b}$$ is dimensionally equal to :