Two particles are executing simple harmonic motion of the same amplitude Aand frequency ω along the x - axis. Their mean position is separated by distance X₀ (X₀ >A). If the maximum separation between them is (X0 + A), the phase difference between their motion is

• π/3

• π/4

• π/6

• π/6

100g of water is heated from 30°C to 50°C ignoring the slight expansion of the water, the change in its internal energy is (specific heat of water is 4184 J/Kg/K)

• 8.4 kJ

• 84 kJ

• 2.1 kJ

• 2.1 kJ

A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heat γ.It is moving with speed v and it suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by 

A mass M, attached to a horizontal spring, executes SHM with an amplitude A₁. When the mass M passes through its mean position than a smaller mass m is placed over it and both of them move together with amplitude A₂. The ratio of (A₁/A₂) is

Water is flowing continuously from a tap having an internal diameter 8 × 10^-3 m. The water velocity as it leaves the tap is 0.4 ms^-1. The diameter of the water stream at a distance 2 × 10^-1 m below the tap is close
to:

• 7.5 x 10^-3 m

• 9.6x 10^-3 m

• 3.6x 10^-3 m

• 3.6x 10^-3 m

Three perfect gases at absolute temperature T₁, T₂ and T₃ are mixed. The masses of molecules are m₁,m₂ and m₃ and the number of molecules is n₁,n₂ and n₃ respectively.Assuming no loss of energy, the final temperature of the mixture is

17.

A Carnot engine operating between temperatures T₁ and T₂ has efficiency 1/6. When T₂ is lowered by 62 K, its efficiency increases to 1/3. Then T₁ and T₂ are, respectively

• 372 K and 330 K

• 330 K and 268 K

• 310 K and 248 K

• 310 K and 248 K

A boat is moving due east in a region where the earth's magnetic field is 5.0 × 10^-5 NA^-1m^-1 due north and horizontal. The boat carries a vertical aerial 2m long. If the speed of the boat is 1.50 ms^-1, the magnitude of the induced emf in the wire of aerial is

• 0.75 mV

• 0.50 mV

• 0.15 mV

• 0.15 mV

A fully charged capacitor C with initial charge q₀ is connected to a coil of self inductance L at t = 0. The time at which the energy is stored equally between the electric and the magnetic fields is

A current I flows in an infinitely long wire with cross-section in the form of a semicircular ring of radius R. The magnitude of the magnetic induction along its axis is