Physics

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

An inductor of 10 mH is connected to a 20 V battery through a resistor of 10 kΩ and a switch. After a long time, when maximum current is set up in the circuit, the current is switched off. The current in the circuit after 1 µs is x/100 mA. Then x is equal to _______. (Take e?¹ = 0.37)

In Young's double slit experiment, if the source of light changes from orange to blue then:

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 << 1m). The particle executes SHM. Its angular frequency of oscillation will be ______ * 10? rad/s if q' = 1 C.

Two capacitors of capacities 2C and C are joined in parallel and charge up to potential V. The battery is removed and the capacitor of capacity C is filled completely with a medium of dielectric constant K. The potential difference across the capacitors will now be:

In the reported figure, two bodies A and B of masses 200g and 800g are attached with the system of springs. Springs are kept in a stretched position with some extension when the system is released. The horizontal surface is assumed to be frictionless. The angular frequency will be _______ rad/s when k = 20 N/m.

Assertion A: If in five complete rotations of the circular scale, the distance travelled on main scale of the screw gauge is 5 mm and there are 50 total divisions on circular scale, then least count is 0.001 cm.
Reason R: Least Count = Pitch / (Total divisions on circular scale)

In the light of the above statement, choose the most appropriate answer from the options given below:

A particle of mass 'm' is moving in time 't' on a trajectory given by r? = 10αt² i? + 5β(t-5) j?. Where α and β are dimensional constants. The angular momentum of the particle become the same as it was for t = 0 at time t = ______ seconds.

If 'f' denotes the ratio of the number of nuclei decayed (Nd) to the number of nuclei at t = 0 (N?) then for a collection of radioactive nuclei, the rate of change of 'f' with respect to time is given as: [λ is the radioactive decay constant]

In the reported figure, there is a cyclic process ABCDA on a sample of 1mol of a diatomic gas. The temperature of the gas during the process A→B and C→D are T? and T? (T? > T?) respectively. Choose the correct option out of the following for work done if processes BC and DA are adiabatic.