1 In an AC circuit, the instantaneous emf and current are given by $e=100\sin30t$ , $i=20\sin\left(30t-\frac{\pi}{4}\right)$ In one cycle of AC , the average power consumed by the circuit and the wattless current are, respectively A) 50 ,10 B) 50 ,0 C) 50/v2 ,0 D) 1000/v2 , 10
2 Two masses m1= 5 kg and m2 = 10 kg connected by an inextensible string over a frictionless pulley , are moving as shown in the figure. The coefficient of friction of horizontal surface is 0.15. The minimum weight m that should be put on top of m2 to stop the motion is A) 18.3 kg B) 10.3 kg C) 43.3 kg D) 27.3 kg
3 From a unifrom circular disc of radius R and mass 9 M, a small disc of radius $\frac{R}{3}$ is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through centre of disc is A) $4MR^{2}$ B) $10MR^{2}$ C) $\frac{40}{9}MR^{2}$ D) $\frac{37}{9}MR^{2}$
4 A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of 1012 per second. What is the force constant of the bonds connecting one atom with other? ( Take, molecular weight of silver=108 and Avogadro number=6.02×1023 g mol-1) A) 7.1 N/m B) 6.4 N/m C) 2.2 N/m D) 5.5 N/m
5 A parallel plate capacitor of capacitance 90pF is connected to a battery of emf 20 V. If a dielectric material of dielectric constant K=$\frac{5}{3}$ is inserted between the plates ,the magnitude of the induced charge will be A) 1.2nC B) 0.3nc C) 2.4nC D) 0.9nC
6 The angular width of the central maximum in a single slit diffraction pattern is 60° .The width of the slit is 1μm. The slit illuminated by monochromatic plane waves. If another slit of same width is made near it, Young's fringes can be observed on a screen placed at a disance 50cm from the slits. If the observed fringe width is 1 cm, what is slit seperation distance? (i.e. distance between the centres of each slit). A) $50\mu m$ B) $25\mu m$ C) $100\mu m$ D) $75\mu m$
7 The reading of the ammeter for a silicon diode in the given circuit is A) 0 B) 15mA C) 11.5mA D) 13.5mA
8 The potential energy of mass m at a distance r from a fixed point O is given by $V(r)=\frac{kr^{2}}{2}$ , where k is a positive constant of appropriate dimensions. This particle is moving in a circular orbit of radius R about the point O. If v is the speed of the particle and L is the magnitude of its angular momentum about O, which of the following statements is (are) true? A) $V= \sqrt{\frac{k}{2m}}R$ B) $V= \sqrt{\frac{k}{m}}R$ C) $L= \sqrt{mk}R^{2}$ D) $L=\sqrt{\frac{mk}{2}}R^{2}$
9 A uniform capillary tube of inner radius r is dipped vertically in to a beaker filled with water. The water rises to a height h in the capillary tube above the water surface in the beaker. The surface tension of the water is $\sigma$ . The angle of contact between water and the wall of the capillary tube is θ . Ignore the mass of water in the meniscus. Which of the following statements is (are) true ? A) For a given material of the capillary tube, h decreases with increase in r B) For a given material of the capillary tube , h is independent of $\sigma$ C) If this experiment is performed in a lift going up with a constant acceleration, then h decreases D) h is proportional to contact angle$\theta$
10 In the figure below , the switches S1 and S2 are closed simultaneously at t=0 and a current starts to flow in the circuit. Both the batteries have the same magnitude of the electromotive force (emf) and the polarities are as indicated in the figure. Ignore mutual inductance between the inductors. The current I in the middle wires reaches its maximum magnitude Imax at time $t=\tau$ . which of the following statements is (are) true ? A) $I_{max}=\frac{V}{2R}$ B) $I_{max}=\frac{V}{4R}$ C) $\tau =\frac{L}{R} In 2$ D) $\tau =\frac{2L}{R} In 2$
11 Two vectors A and B are defined as $A= a\hat{i}$ and $B= a (\cos wt\hat{i}+\sin w\hat{j})$, where a is a constant and $w=\frac{\pi}{6}rad $$s^{-1}$ . If $\mid A+B\mid =\sqrt{3}\mid A-B\mid$ at time $t= \tau$ for the first time, the value of $\tau$ in seconds, is A) 3.00 s B) 2.00 s C) 5.00 s D) 7.00 s
12 Two men are walking along a horizontal straight line in the same direction.The man in front walks at speed 1.0 ms-1 and the man behind walks at a speed 2.0 ms-1 . A third man is standing at a height 12 m above the same horizontal line such that all three men are in a vertical plane. The two walking men are blowing identical whistles which emit a sound of frequency 1430Hz. The speed of sound in air 330 ms-1. At the instant , when the moving men are 10 m apart, the stationary man is equidistant from them. The frequency of beats in Hz, heard by the stationary man at this instant, is.... A) 3 Hz B) 5 Hz C) 7 Hz D) 6 Hz
13 A particle of mass m is initially at rest at the origin . It is subjected to a force and starts moving along the X-axis . Its kinectic energy K changes with time as $\frac{\text{d}K}{\text{d}t}=\gamma t$ , where $\gamma $ is a positive constant of appropriate dimensions. Which of the following statements is (are) true? A) The force applied on the particle is constant B) The speed of the particle is proportional to time C) The distance of the particle from the origin increases linearly with time. D) The force is conservative.
14 An infinitely long thin non-conducting wire is parallel to the Z-axis and carries a uniform line charge density λ . It pierces a thin non-conducting spherical shell of radius R in such a way that the arc PQ subtends an angle 120° at the centre O of the spherical shell, as shown in the figure. The permittivity of free space is ε0 . Which of the following statements is (are) true? A) The electric flux through the shell is $\sqrt{3}R\lambda /\epsilon_{0}$ B) The z-component of the electric field is zero at all the points on the surface of the shell. C) The electric flux through the shell is $\sqrt{2}R\lambda /\epsilon_{0}$ D) The electric field is normal to the surface of the shell at all points.
15 A particle of mass 10-3 kg and charge 1.0 C is initially at rest. At time t=0, the particle comes under the influence of an electric field E (t)= E0 sin ωt $\hat{i}$, where E0 = 1.0N C-1 and ω=103 rad s-1 . Consider the effect of only the electrical force on the particle . Then , the maximum speed in ms-1 , attained by the particle at subsequent times is.......... A) 1 B) 2 C) 1.5 D) 3
