1 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 $\frac{dr}{r}$ is A) $\frac{Ka}{mg}$ B) $\frac{Ka}{3mg}$ C) $\frac{mg}{3Ka}$ D) $\frac{mg}{Ka}$
2 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
3 A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the n th power of R. If the period of rotation of the particle is T, then A) $T\propto R^{\frac{3}{2}}$ For any n B) $T\propto R^{\frac{n}{2}}$ C) $T\propto R^{\frac{n}{2}+1}$ D) $T\propto R^{\frac{(n+1)}{2}}$
4 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) $\frac{37}{9}MR^{2}$
5 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) $\frac{mg}{Ka}$
6 The mass of a hydrogen molecule is 3.32 x10-27 kg. If 1023hydrogen molecules strike per second, a fixed wall of area 2 cm2 at an angle of 45° to the normal and rebound elastically with a speed of 103 m/s, then the pressure on the wall is nearly A) $2.35\times 10^{3} N/m^{2}$ B) $4.70\times 10^{3} N/m^{2}$ C) $4.70\times 10^{2} N/m^{2}$ D) $2.35\times 10^{2} N/m^{2}$
7 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
8 An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii re,rp,rα is repectively, in a unifrom magnetic field B. The relation between re,rp, rα is>> A) $r_{e}\gt r_{p}= r_{\alpha}$ B) $r_{e}\lt r_{p}= r_{\alpha}$ C) $r_{e}\lt r_{p}\lt r_{\alpha}$ D) $r_{e}\lt r_{\alpha}\lt r_{p}$
9 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) $75\mu m$
10 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
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 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.
13 In an experiment to measure the speed of sound by a resonating air column, a turning fork of frequency 500Hz is used. The length of the air column is varied by changing the level of water in the resonance tube . Two successive resonances are heard at air columns of length 50.7cm and 83.9 cm . Which of the following statements is (are) true? A) The speed of sound determined from this experiment is $332 ms^{-1}$ B) The end correction in this experiment is 0.9 cm C) The wavelength of the sound wave is 66.4 cm D) The resonance at 50.7 cm corresponds to the fundamental harmonic
14 One mole of monoatomic ideal gas undergoes an adiabatic expansion in which its volume becomes eight times its initial value. If the initial temperature of the gas is 100K and the universal gas constant R= 8.0 j mol-1 K-1 , the decrease in its internal energy in joule, is .............. A) 450 J B) 900 J C) 850 J D) 750 J
15 Consider a hydrogen -like ionised atom with atomic number Z , with a single electron. In the emission spectrum of atom, the photon emitted in the n= 2 to n=1 transition has energy 74.8 eV higher than the photon emitted in the n=3 to n=2 transition.The ionisation energy of the hydrogen atom is 13.6 eV. The value of Z is.......... A) 3 B) 6 C) 4 D) 2
