The value of aluminium susceptibility is 2.2 $$\times$$ 10^$$-$$5. The percentage increase in the magnetic field if space within a current carrying toroid is filled with aluminium is $${x \over {{{10}^4}}}$$. Then the value of x is _________________.

A particle of mass 1 mg and charge q is lying at the mid-point of two stationary particles kept at a distance '2 m' when each is carrying same charge 'q'. If the free charged particle is displaced from its equilibrium position through distance 'x' (x < < 1 m). The particle executes SHM. Its angular frequency of oscillation will be ____________ $$\times$$ 10⁵ rad/s if q² = 10 C².

An electric bulb rated as 200 W at 100 V is used in a circuit having 200 V supply. The resistance 'R' that must be put in series with the bulb so that the bulb delivers the same power is _____________ $$\Omega$$.

A pendulum bob has a speed of 3 m/s at its lowest position. The pendulum is 50 cm long. The speed of bob, when the length makes an angle of 60$$^\circ$$ to the vertical will be (g = 10 m/s²) ____________ m/s.