Instructions

In the figure a container is shown to have a movable (without friction) piston on top. The container and the piston are all made of perfectly insulating material allowing no heat transfer between outside and inside the container. The container is divided into two compartments by a rigid partition made of a thermally conducting material that allows slow transfer of heat. The lower compartment of the container is filled with 2 moles of an ideal monatomic gas at 700 K

and the upper compartment is filled with 2 moles of an ideal diatomic gas at 400 K. The heat capacities per mole of an ideal monatomic gas are $$C_v = \frac{3}{2}R, C_P = \frac{5}{2}R,$$ and those for an ideal diatomic gas are $$C_v = \frac{5}{2}R, C_P = \frac{7}{2}R.$$

Question 11

Consider the partition to be rigidly fixed so that it does not move. When equilibrium is achieved, the final temperature of the gases will be

Question 12

Now consider the partition to be free to move without friction so that the pressure of gases in both compartments is the same. Then total work done by the gases till the time they achieve equilibrium will be

Instructions

A spray gun is shown in the figure where a piston pushes air out of a nozzle. A thin tube of uniform cross section is connected to the nozzle. The other end of the tube is in a small liquid container. As the piston pushes air through the nozzle, the liquid from the container rises into the nozzle and is sprayed out. For the spray gun shown, the radii of the piston and the nozzle are 20 mm and 1mm, respectively. The upper end of the container is open to the atmosphere.

Question 13

If the piston is pushed at a speed of $$5 mms^{-1}$$, the air comes out of the nozzle with a speed of

Question 14

If the density of air is $$\rho_a$$ and that of the liquid $$\rho_l$$, then for a given piston speed the rate (volume per unit time) at which the liquid is sprayed will be proportional to

Instructions

The figure shows a circular loop of radius a with two long parallel wires (numbered 1 and 2) all in the plane of the paper. The distance of each wire from the centre of the loop is d. The loop and the wires are carrying the same current I. The current in the loop is in the counterclockwise direction if seen from above.

Question 15

When $$d \approx a$$ but wires are not touching the loop, it is found that the net magnetic field on the axis of the loop is zero at a height h above the loop. In that case

Question 16

Consider $$d \gg a$$, and the loop is rotated about its diameter parallel to the wires by $$30^\circ$$ from the position shown in the figure. If the currents in the wires are in the opposite directions, the torque on the loop at its new position will be (assume that the net field due to the wires isÂ constant over the loop)

Instructions

For the following questions answer them individually

Question 17

Four charges $$Q_1, Q_2, Q_3$$ and $$Q_4$$ of same magnitude are fixed along the x axis at x = âˆ’2a, âˆ’a, +a and +2a, respectively. A positive charge q is placed on the positive y axis at a distance b > 0. Four options of the signs of these charges are given in List I. The direction of the forces on the charge q is given in List II. Match List I with List II and select the correct answer using the code given below the lists.

Question 18

Four combinations of two thin lenses are given in List I. The radius of curvature of all curved surfaces is r and the refractive index of all the lenses is 1.5. Match lens combinations in List I with their focal length in List II and select the correct answer using the code given below the lists.

Choices:

Question 19

A block of mass $$m_1 = 1 kg$$ another mass $$m_2 = 2 kg$$, are placed together (see figure) on an inclined plane with angle of inclination $$\theta$$. Various values of $$\theta$$ are given in List I. The coefficient of friction between the block $$m_1$$ and the plane is always zero. The coefficient of static and dynamic friction between the block $$m_2$$ and the plane are equal to $$\mu = 0.3.$$ In List II expressions for the friction on block $$m_2$$ are given. Match the correct expression of the friction in List II with the angles given in List I, and choose the correct option. The acceleration due to gravity is denoted by g.

[Useful information :$$\tan (5.5^\circ) \approx 0.1; \tan(11.5^\circ) \approx 0.2; \tan(16.5^\circ) \approx 0.3]$$

Choices:

Question 20

A person in a lift is holding a water jar, which has a small hole at the lower end of its side. When the lift is at rest, the water jet coming out of the hole hits the floor of the lift at a distance of 1.2 m from the person. In the following, state of the liftâ€™s motion is given in List I and the distance where the water jet hits the floor of the lift is given in List II. Match the statements from List I with those in List II and select the correct answer using the code given below the list.

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