A rectangular block of mass $$5 \mathrm{~kg}$$ attached to a horizontal spiral spring executes simple harmonic motion of amplitude $$1 \mathrm{~m}$$ and time period $$3.14 \mathrm{~s}$$. The maximum force exerted by spring on block is _________ N

A square loop of side $$2.0 \mathrm{~cm}$$ is placed inside a long solenoid that has 50 turns per centimetre and carries a sinusoidally varying current of amplitude $$2.5 \mathrm{~A}$$ and angular frequency $$700 ~\mathrm{rad} ~\mathrm{s}^{-1}$$. The central axes of the loop and solenoid coincide. The amplitude of the emf induced in the loop is $$x \times 10^{-4} \mathrm{~V}$$. The value of $$x$$ is __________.

$$ \text { (Take, } \pi=\frac{22}{7} \text { ) } $$

If the maximum load carried by an elevator is $$1400 \mathrm{~kg}$$ ( $$600 \mathrm{~kg}$$ - Passengers + 800 $$\mathrm{kg}$$ - elevator), which is moving up with a uniform speed of $$3 \mathrm{~m} \mathrm{~s}^{-1}$$ and the frictional force acting on it is $$2000 \mathrm{~N}$$, then the maximum power used by the motor is __________ $$\mathrm{kW}\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)$$

An electron revolves around an infinite cylindrical wire having uniform linear charge density $$2 \times 10^{-8} \mathrm{C} \mathrm{m}^{-1}$$ in circular path under the influence of attractive electrostatic field as shown in the figure. The velocity of electron with which it is revolving is ___________ $$\times 10^{6} \mathrm{~m} \mathrm{~s}^{-1}$$. Given mass of electron $$=9 \times 10^{-31} \mathrm{~kg}$$