Physics

A beam of electrons of energy E scatters from a target having atomic spacing of IÅ °. The first maximum intensity occurs at θ = 60°. Then E (in eV) is (Planck constant h = electron mass m = 9.1 * 10?³¹ kg )

Two concentric circular coils, C₁ and C₂ are placed in the XY plane. C₁ has 500 turns, and a radius of 1 cm. C₂ has 200 turns and radius of 20 cm. C₂ carries a time dependent current I(t) = (5t² - 2t + 3)A where t is in s. The emf induced in C₁ (in mV ), at the instant t = 1 s is x/4. The value of x is

A particle of mass 200MeV/c² collides with a hydrogen atom at rest. Soon after the collision the particle comes to rest, and the atom recoils and goes to its first excited state. The initial kinetic energy of the particle (in eV) is N/4. The value of N is: (Given the mass of the hydrogen atom to be 1GeV/c²)

A force F = (î + 2ĵ + 3k)N acts at a point (4î + 3ĵ – k)m. Then the magnitude of torque about the point (î + 2ĵ + k)m will be √xN m. The value of x is

Two capacitors of capacitances C and 2C are charged to potential differences V and 2 V, respectively. These are then connected in parallel in such a manner that the positive terminal of one is connected to the negative terminal of the other. The final energy of this configuration is:

An electrical power line, having a total resistance of 2Ω, delivers 1 kW at 220 V. The efficiency of the transmission line is approximately:

Activities of three radioactive substances A, B and C are represented by the curves A, B and C in the figure. Then their half lives T₁(A): T₁(B): T₁(C) are in the ratio:

A helicopter rises from rest on the ground vertically upwards with a constant acceleration g. A food packet is dropped from the helicopter when it is at a height h. The time taken by the packet to reach the ground is close to [ g is the acceleration due to gravity]:

Assume that the displacement (s) of air is proportional to the pressure difference (Ap) created by a sound wave. Displacement (s) further depends on the speed of sound (v), density of air ( ρ ) and the frequency (f). If Ap ~ 10 Pa, v ~ 300 m/s, p ~ π11g/m³ and f ~ 1000 Hz, then s will be of the order of (take the multiplicative constant to be 1)

A square loop of side 2a, and carrying current I, is kept in XZ plane with its centre at origin. A long wire carrying the same current I is placed parallel to the z axis and passing through the point (0, b, 0), (b >> a). The magnitude of the torque on the loop about z - axis is given by: