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1.

The instantaneous voltage at three terminals marked X, Y and Z are given by VX= V0 sinωt.

$V_{Y}=V_{0}\sin(\omega t+\frac{2\pi}{3}) and$

$V_{Z}=V_{0}\sin(\omega t+\frac{4\pi}{3})$

An ideal voltmeter is configured to read rms value of the potential difference between its terminals. It is connected between points X and Y and then between Y and Z . The reading (s) of the voltmeter will be

A) $V_{YZ}^{rms}=V_{0}\sqrt{\frac{1}{2}}$

B) $V_{XY}^{rms}=V_{0}\sqrt{\frac{3}{2}}$

C) independent of the choice of the two terminals

D) $V_{XY}^{rms}=V_{0}$

2.

A uniform magnetic field B exists in the region between x=0 and $x=\frac{3R}{2}$

(region 2 in the figure)pointing normally into the plane of the paper. A particle with charge +Q and momentum p directed along X-axis enters region 2 from region 1 at point P1(y=-R)

which of the following option(s) is/are correct?

A) when the particle re-enters region 1 through the longest possible path in region 2 the magnitude of the change in its linear momentum between point $P_{1}$ and the farthest point from Y-axis is $\frac{p}{\sqrt{2}}$

B) For $B=\frac{8}{13}\frac{p}{QR}$ , the particle will enter region 3 through the point $P_{2}$ on X-axis

C) For B>$\frac{2}{3}\frac{p}{QR}$ , the particle will re enter region 1

D) For a fixed B, particles of same range Q and same velocity v, the distance between the point $P_{1}$ , and the point of re entry into region 1 is inversely proportional to the mass of the particle

3.

A source of constant voltage V is connected to a resistance R and two ideal inductors L1 and L2 through a switch S as shown. There is no mutual inductance between the two inductors. The switch S is initially open. At t=0, the switch is closed and current begins to flow. Which of the following options is/are correct?

A) After a long time the current through $L_{1}$ will be $\frac{V}{R}\frac{L_{2}}{L_{1}+L_{2}}$

B) After a long time , the current through $L_{2}$ will be $\frac{V}{R}\frac{L_{1}}{L_{1}+L_{2}}$

C) The ratio of the currents through $L_{1}$ and $L_{2}$ is fixed at all times (t>0)

D) At t=0 the current through the resistance $R is\frac{V}{R}$

4.

A wheel of radius R and mass M is placed at the bottom of a fixed step of height R as shown in the figure. A constant force is continuously applied on the surface of the wheel so that it just climbs the step without slipping. Consider the torque  $\tau$ about an axis normal to the plane of the paper passing through the point Q. Which of the following options is/are correct ?

A) If the force is applied normal to the circumference at point P then $\tau$ is zero

B) if the force is applied tangentially at point S then $\tau\neq 0$ but the wheel never climbs the step

C) If the force is applied at point P tangentially , then $\tau$ decreases continously as the wheel climbs

D) If the force is applied normal to the circumfernce at point X , then $\tau$ is constant

5.

A rigid uniform bar AB of length L is slipping from its vertical position on a frictionless floor (as shown in the figure). At some instant of time, the angle made by the bar with the vertical is θ. Which of the following statements about its motion is/are correct?

A) Instantaneous torque about the point in contact with the floor is proportional to $\sin\theta$

B) The trajectory of the point A is parabola

C) The midpoint of the bar will fall vertically downward

D) When the bar makes an angle $\theta$ with the vertical, the displacement of its mid point from intial position is proportional to $(1-\cos\theta)$

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