Instructions

For the following questions answer them individually

Question 11

In the circuit shown below, the key is pressed at time t=0. Which of the following statement(s) is(are) true?

Question 12

A block with mass M is connected by a massless spring with stiffness constant k to a rigid wall and moves without friction on a horizontal surface. The block oscillates with small amplitude A about an equilibrium position $$x_0$$. Consider two cases:

(i) when the block is at $$x_0$$; and

(ii) when the block is at $$x = x_0 + A$$.

In both thecases, a particle with mass m(< M) is softly placed on the block after which they stick to each other. Which of the following statement(s) is(are) true about the motion after the mass mis placed on the mass M ?

Question 13

While conducting the Youngâ€™s double slit experiment, a student replaced the two slits with a large opaque plate in the x-y plane containing two small holes that act as two coherent point sources $$(S_1, S_2)$$ emitting light of wavelength 600 nm. The student mistakenly placed the screen parallel to the x-z plane (for z > 0) at a distance D = 3 m from the mid-point of S,S,, as shown schematically in the figure. The distance between the sources d = 0.6003 mm. The origin O is at the intersection of the screen and the line joining $$S_1, S_2$$. Which of the following is(are) true of the intensity pattern on the screen?

Question 14

A rigid wire loop of square shape having side of length L and resistance R is moving along the x-axis with a constant velocity $$v_0$$ in the plane of the paper. At t = 0, the right edge of the loop enters a region of length 3L where there is a uniform magnetic field $$B_0$$, into the plane of the paper, as shown in the figure. For sufficiently large $$v_0$$, the loop eventually crosses the region. Let x be the location of the right edge of the loop. Let v(x), I(x) and F(x) represent the velocity of the loop, current in the loop, and force on the loop, respectively, as a function of x. Counter-clockwise current is taken as positive.

Which of the following schematic plot(s) is(are) correct? (Ignore gravity)

Instructions

PARAGRAPH 1

A frame of reference that is accelerated with respect to an inertial frameof reference is called a non-inertial frame of reference. A coordinate system fixed on a circular disc rotating about a fixed axis with a constant angular velocity $$\omega$$ is an example of a non-inertial frame of reference. The relationship between the force $$\overrightarrow{F}_{rot}$$ experienced by a particle of mass m moving on the $$\overrightarrow{F}_{in}$$ experienced by the particle in an inertial frame of reference is

$$ \overrightarrow{F}_{rot} = \overrightarrow{F}_{in} + 2m(\overrightarrow{V}_{rot} \times \overrightarrow{\omega}) + m(\overrightarrow{\omega} \times \overrightarrow{r}) \times \overrightarrow{\omega}$$,

where $$\overrightarrow{v}_{rot}$$ is the velocity of the particle in the rotating frameof reference and $$\overrightarrow{r}$$. is the position vector of the particle with respect to the centre of the disc.

Now consider a smooth slot along a diameter of a disc of radius R rotating counter-clockwise with a constant angular speed $$\omega$$ about its vertical axis through its center. We assign a

coordinate system with the origin at the center of the disc, the x-axis along the slot, the y-axis perpendicular to the slot and the z-axis along the rotation axis $$(\overrightarrow{\omega} = \omega \hat{k})$$. A small block of mass m is gently placed in the slot at $$\overrightarrow{r} = \left(\frac{R}{2}\right)\hat{i}$$ at t = 0 and is constrained to move only along the slot.

Instructions

PARAGRAPH 2

Consider an evacuated cylindrical chamber of height h having rigid conducting plates at the ends and an insulating curved surface as shownin the figure. A number of spherical balls made

of a light weight and soft material and coated with a conducting material are placed on the bottom plate. The balls have a radius r<<h. Nowa high voltage source (HV) is connected across

the conducting plates such that the bottom plate is at $$+ V_0$$ and the top plate at $$- V_0$$. Due to their conducting surface, the balls will get charged, will become equipotential with the plate and are repelled by it. The balls will eventually collide with the top plate, where the coefficient of restitution can be taken to be zero due to the soft nature of the material of the balls. The electric field in the chamber can be considered to be that of a parallel plate capacitor. Assume that there are no collisions between the balls and the interaction between them is negligible. (Ignore gravity)

Question 18

The average current in the steady state registered by the ammeter in the circuit will be

Instructions

For the following questions answer them individually

Question 19

For the following electrochemical cell at 298 K,

$$Pt(s) \mid H_2(g, 1 bar) \mid H^+(aq, 1M) \parallel M^{4+}(aq), M^{2+}(aq) \mid Pt(s)$$

$$E_{cell} = 0.092 V$$ and when $$\frac{[M^{2+}(aq)]}{[M^{4+}(aq)]} = 10^x$$.

Given : $$E_{\frac{M^{4+}}{M^{2+}}}^{0} = 0.15 V; 2.303 \frac{RT}{F} = 0.059 V$$

The value of x is

Question 20

The qualitative sketches I, II and III given below show the variation of surface tension with molar concentration of three different aqueous solutions of KCl, $$CH_3OH$$ and $$CH_3(CH_2)_{11}OSO_3{^-Na^+}$$ at room temperature. The correct assignment of the sketches is