Two narrow bores of diameter 5.0 mm and 8.0 mm are joined together to form a U-shaped tube open at both ends. If this U-tube contains water, what is the difference in the level of two limbs of the tube. [Take surface tension of water T = 7.3 $$\times$$ 10^$$-$$2 Nm^$$-$$1, angle of contact = 0, g = 10 ms² and density of water = 1.0 $$\times$$ 10³ kg m^$$-$$3]

An electric appliance supplies 6000 J/min heat to the system. If the system delivers a power of 90W. How long it would take to increase the internal energy by 2.5 $$\times$$ 10³ J ?

An inductor coil stores 64 J of magnetic field energy and dissipates energy at the rate of 640 W when a current of 8A is passed through it. If this coil is joined across an ideal battery, find the time constant of the circuit in seconds :

A series LCR circuit driven by 300 V at a frequency of 50 Hz contains a resistance R = 3 k$$\Omega$$, an inductor of inductive reactance X_L = 250 $$\pi$$$$\Omega$$ and an unknown capacitor. The value of capacitance to maximize the average power should be : (Take $$\pi$$² = 10)