Physics

An inductor and a resistor are connected to an ac supply of 120 V, 50 Hz. The resistance of the resistor is 20Ω. If the voltages leads the current by a phase difference of 45°, find the inductance of the inductor.

Write the value of current i₃ (in mA) in the circuit shown in the figure.

A vernier calliper whose 10 vernier scale divisions coincide with 9 main scale divisions is used to take a reading. Each main scale division is 1 mm. Before taking the reading it is observed that the 4^th division of the vernier scale coincides with the main scale and zero of main scale is behind zero of vernier scale. When the reading is taken using this vernier calliper, the main scale reads 2.5 cm and the 7^th division of the vernier scale coincides with the main scale. Find the final value of the measurement.

A massless metal plate is placed on a horizontal tabletop lubricated with oil. The sheet is a square of side length $\mathcal{l}$ = 1.0m and the oil layer has thickness h = 1.0mm. Initially one edge of the sheet coincides with one edge of the table. The sheet is pulled outwards without rotation with a constant force F = 15 N. If coefficient of viscosity of the oil is $\eta$ = 0.2 N-s/m², how long (in second) will it take to pull half of the sheet out of the table?

Two particles are executing SHM which are described by the equations x₁ = asin(ωt + π/6) and x₂ = asin(ωt + π/4). Find the minimum time interval between the particles to cross their mean position.

A particle of mass 2 kg is moving in the direction of positive x-axis. Initial velocity of the particle is 1 m/s. The instantaneous power vs time graph of the particle is shown in the figure. Find the velocity of the particle at 7 seconds.

A string of mass per unit length $\mu$  is clamped at both ends such that one end of the string is at x = 0 and the other end at x = L. When string vibrates in fundamental mode, amplitude of the midpoint of string is a and tension is string is F. Find the total oscillation energy (in J) stored in the string.

(Use L = 1m, F = 10 N, a =   $\frac{1}{\pi }m)$

In an imaginary electric field, the electric potential energy of an electron at a distance r from the centre of force field is given by U = kr², where k is a positive constant of appropriate dimensions. If the electron is moving in a circular orbit of radius r about the centre, then the orbital time period of the electron is proportional to:

A railway track (made of iron) is laid in winter when the average temperature is $18°C.$  The track consists of sections of 12.0m placed on after the other. How much gap (in cm) should be left between two such sections so that there is no compression during summer when the maximum temperature goes to $48°C?$  Coefficient of linear expansion of iron = 11 * $10^{-6}/°C$ .

A source of light emits monochromatic visible light of wavelength 500 nm. The source emits light of power 100W. The number of photons emitted per sec of the visible light of the given wavelength is: $(\mathrm{h}\mathrm{c}=1240\mathrm{e}\mathrm{V}.\mathrm{n}\mathrm{m})$