PART I : PHYSICS
Q.1 A flat plate is moving normal to its plane through a gas under the action of a constant force F. The gas is kept at a very low pressure. The speed of the plate v is much less than the average speed u of the gas molecules. Which of the following options is/are true?
[A] The pressure difference between the leading and trailing faces of the plate is proportional to uv
[B] The resistive force experienced by the plate is proportional to v
[C] The plate will continue to move with constant non-zero acceleration, at all times
[D] At a later time the external force F balances the resistive force
Q.2 A block of mass M has a circular cut with a frictionless surface as shown. The block rests on the horizontal frictionless surface of a fixed table. Initially the right edge of the block is at x = 0, in a co-ordinate system fixed to the table. A point mass m is released from rest at the topmost point of the path as shown and it slides down. When the mass loses contact with the block, its position is x and the velocity is v. At that instant, which of the following options is/are correct?
[A] The position of the point mass m is:
[B] The velocity of the point mass m is:
[C] The x component of displacement of the center of mass of the block M is: v=
[D] The velocity of the block M is:
Q.3 A block M hangs vertically at the bottom end of a uniform rope of constant mass per unit length. The top end of the rope is attached to a fixed rigid support at O. A transverse wave pulse (Pulse 1) of wavelength λ0 is produced at point O on the rope. The pulse takes time TOA to reach point A. If the wave pulse of wavelength λ0 is produced at point A (Pulse 2) without disturbing the position of M it takes time TAO to reach point O. Which of the following options is/are correct?
[A] The time TAO = TOA
[B] The velocities of the two pulses (Pulse 1 and Pulse 2) are the same at the midpoint of rope
[C] The wavelength of Pulse 1 becomes longer when it reaches point A
[D] The velocity of any pulse along the rope is independent of its frequency and wavelength
Q.4 A human body has a surface area of approximately 1 m2. The normal body temperature is 10 K above the surrounding room temperature T0. Take the room temperature to be T0 = 300K. Take the room temperature to be(where is the Stefan-Boltzmann constant). Which of the following options is/are correct?
[A] The amount of energy radiated by the body in 1 second is close to 60 Joules
[B] If the surrounding temperature reduces by a small amount ∆ then to maintain the same body temperature the same (living) human being needs to radiate
[C] Reducing the exposed surface area of the body (e.g. by curling up) allows humans to maintain the same body temperature while reducing the energy lost by radiation
[D] If the body temperature rises significantly then the peak in the spectrum of electromagnetic radiation emitted by the body would shift to longer wavelengths
Q.5 A circular insulated copper wire loop is twisted to form two loops of area A and 2A as shown in the figure. At the point of crossing the wires remain electrically insulated from each other. The entire loop lies in the plane (of the paper). A uniform magnetic field points into the plane of the paper. At T= 0, the loop starts rotating about the common diameter as axis with a constant angular velocity ω in the magnetic field. Which of the following options is/are correct?
[A] The emf induced in the loop is proportional to the sum of the areas of the two loops
[B] The amplitude of the maximum net emf induced due to both the loops is equal to the amplitude of maximum emf induced in the smaller loop alone
[C] The net emf induced due to both the loops is proportional to cos ωt
[D] The rate of change of the flux is maximum when the plane of the loops is perpendicular to plane of the paper
Q.6 In the circuit shown, They are connected in series with an a.c. source V= V0 sin ωt as shown. Which of the following options is/are correct?
[A] The current will be in phase with the voltage if