IIT JEE Physics Final Revision Set 37

1. A student performed the experiment to measure the speed of sound in air using resonance air-column method. Two resonances in the air-column were obtained by lowering the water level. The resonance with the shorter air-column is the first resonance and that with the longer air-column is the second resonance.
Then -

(A) the intensity of the sound heard at the first resonance was more than that at the second resonance
(B) the prongs of the tuning fork were kept in a horizontal plane above the resonance tube
(C) the amplitude of vibration of the ends of the prongs is typically around 1 cm
(D) the length of the air-column at the first resonance was somewhat shorter than 1/4th of the wavelength of the sound in air.

2. Column II gives certain systems undergoing a process. Column I suggests changes in some of the
parameters related to the system. Match the statements in Column I to the appropriate process(es) from
Column II.



Column I
(A) The energy of the system is increased
(B) Mechanical energy is provided to the system, which is converted into energy of random motion of its parts
(C) Internal energy of the system is converted into its mechanical energy
(D) Mass of the system is decreased



Column II

(p) System : A capacitor, initially uncharged
Process : It is connected to a battery


(q) System : A gas in an adiabatic container fitted with an adiabatic piston
Process : The gas is compressed by pushing the piston

(r) System : A gas in a rigid container
Process : The gas gets cooled due to colder atmosphere surrounding it

(s) System : A heavy nucleus, initially at rest
Process : The nucleus fissions into two fragments of nearly equal masses and some
neutrons are emitted
(t) System : A resistive wire loop
Process : The loop is placed in a time varying magnetic field perpendicular to its plane



3. A solid sphere of radius R has a charge Q distributed in its volume with a charge density ρ = κr^a, where κ
and a are constants and r is the distance from its centre. If the electric field at r = R/2 is (1/8) times that at r = R, find the value of a.(in integer values)

4. A steady current I goes through a wire loop PQR having shape of a right angle triangle with PQ = 3x,
PR = 4x and QR = 5x. If the magnitude of the magnetic field at P due to this loop is k = (μ₀I/48πx), find the value of k (answer is to be in integers)

5.Two soap bubbles A and B are kept in a closed chamber where the air is maintained at pressure 8 N/m². The radii of bubbles A and B are 2 cm and 4 cm, respectively. Surface tension of the soap-water used to make bubbles is 0.04 N/m. Find the ratio nB/nA, where nA and nB are the number of moles of air in bubbles
A and B, respectively. [Neglect the effect of gravity.]

Source: 2009 JEE paper 2