1 The dipole moment of a circular loop carrying a current I, is m and the magnetic field at the centre of the loop is B1. When the dipole moment is doubled by keeping the current costant, the magnetic field at the centre of the loop is B2. The ratio B1/B2 A) 2 B) $\sqrt{2}$ C) $\sqrt{3}$ D) $\frac{1}{\sqrt{2}}$
2 A particle is moving in a circular path of radius a under the action of an attractive potential $U=-\frac{k}{2r^{2}}$ , Its total energy is A) $-\frac{k}{4a^{2}}$ B) 0 C) $\frac{K}{2a^{2}}$ D) $-\frac{3k}{2a^{2}}$
3 A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area a floats on the surface of the liquid, covering entire cross- section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere, ($\frac{\text{d}r}{\text{}r}$) is A) $\frac{Ka}{mg}$ B) $\frac{Ka}{3mg}$ C) $\frac{mg}{3Ka}$ D) $\frac{mg}{Ka}$
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 Two moles of an ideal monoatomic gas occupies a volume V at 27° C. The gas expands adiabatically to a Volume 2 V. Calculate(i) the final temperature of the gas and (ii) change in its internal energy. A) (i)189 K (ii) 2.7 KJ B) (i) 195 K (ii) -2.7 KJ C) (i) 189 K (ii) -2.7 KJ D) (i) 195 K (ii) 2.7 KJ
6 Two batteries with emf 12V and 13V are connected in parallel across a load resistor of 10 Ω . The internal resistances of the two batteries are 1Ω and 2Ω, respectively. The voltage across the load lies between A) 11.6 V and 11.7 V B) 11.5 V and 11.6 V C) 11.4 V and 11.5 V D) 11.7 V and 11.8 V
7 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) $\tau =\frac{2L}{R} In 2$
8 One mole of a monoatomic ideal gas undergoes a cyclic process as shown in the figure (where ,V is the volume and T is the temperature ). Which of the statements below is (are) true? A) Process I is an isochoric process B) In process II, gas absorbs heat C) In process IV, gas releases heat D) Processes I and III are not isobaric
9 Two infinitely long straight wires lie in the xy-plane along the lines x=± R. The wire located at x=± R carries a constant current I1 and the wire located at x= -R carries a constant cureent I2. A circular loop of radius R is suspended with its centre at (0,0,√3R) and in a plane parallel to the xy-plane . This loop carries a constant current I in the clockwise direction as seen from above the loop.The current in the wire taken to be postive , if it is in the +$\hat{j}$- direction . Which of the following statements regarding the magnetic field B is (are) true ? A) If $l_{1}=l_{2}$, then B cannot be equal to zero at the origin (0,0,0) B) If $l_{1}\gt0$ and $l_{2}\lt0$ , then B can be equal to zero at the origin (0,0,0) C) If $l_{1}\lt0$ and $l_{2}\lt0$, then B can be equal to zero at the origin (0,0,0) D) If $l_{1}=l_{2}$ , then the z-component of the magnetic field at the centre of the loop is $(-\frac{\mu_{0}l}{2R})$
10 Sunlight of intensity 1.3kWm-2 is incident normally on a thin convex lens of focal length 20 cm. Ignore the energy loss of light due to the lens and assume that the lens aperture size is much smaller than its focal length. The average intensity of light , in kW m-2, at a distance 22 cm from the lens on the other side is ..... A) $130kWm^{-2}$ B) $140kWm^{-2}$ C) $120kWm^{-2}$ D) $150kWm^{-2}$
11 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.
12 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.
13 A ball is projected from the ground at an angle of 45° with the horizontal surface . It reaches a maximum height of 120m and returns to the ground. Upon hitting the ground for the first time, it loses half of its kinetic energy . Immediately after the bounce , the velocity of the ball makes an angle of 30° with the horizontal surface . The maximum height it reaches after the bounce, in metres, is......... A) 40 B) 25 C) 30 D) 15
14 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
15 In a photoelectric experiment , a parallel beam of monochromatic light with power of 200 W is incident on a perfectly absorbing cathode of work function 6.25 eV . The frequency of light is just above the threshold frequency, so that the photoelectrons are emitted with negligible kinetic energy. Assume that the photoelectron emission efficiency is 100% . A potential difference of 500 V is applied between the cathode and the anode. All the emitted electrons are incident normally on the anode and are absorbed. The anode experiences a force F= n × 10-4 N due to the impact of the eletrons. The value of n is .................(Take mass of the electron, me =9× 10-31 kg and eV = 1.6 × 10-19 J) A) 26 B) 24 C) 42 D) 12
