Q. Consider a spherical shell of radius R with a total charge $+$q uniformly spread on its surface(center of the chell lies at the origin $x=0$). Two point charges, $+q$ and $-q$ are brought, one after the other, from far away and placed at $x=-a/2$ and $x=+a/2$ $(a<R)$, respectively. Magnitude of the work done in this process is$?$

1. $(Q+q{)}^2.4\pi {\epsilon }_{0}a$
2. $q^2/4\pi {\epsilon }_{0}a$
3. Zero
4. $Qq/4\pi {\epsilon }_{0}a$

Q. A body moves in a circular orbit of radius R under the action of a central force. Potential due to the central force is given by $V\left(r\right)=kr$(k is a positive constant). Period of revolution of the body is proportional to.

1. $R^{1/2}$
2. $R^{-3/2}$
3. $R^{-1/2}$
4. $R^{-5/2}$

Q. Consider two thermometers $T_1$ and $T_2$ of equal length which can be used to measure temperature over the range ${\theta }_1$ and ${\theta }_2$. $T_1$ contains mercury as thermometric liquid while $T_2$ contains bromine. The volumes of the two liquids are the same at the temperature ${\theta }_1$. The volumetric coefficients of expansion of mercury and bromine are $18\times {10}^{-5}{K}^{-1}$ and $108\times {10}^{-5}{K}^{-1}$, respectively. The increase in length of each liquid is the same for the same increase in temperature. If the diameters of the capillary tubes if the two thermometers are $d_1$ and $d_2$ respectively, then the ratio $d_1:d_2$ would be closest to.

1. $6.0$
2. $0.5$
3. $2.5$
4. $0.4$

Q. What are the charges stored in the $1\mu F$ and $2\mu F$ capacitors in the circuit below, once the currents become steady?

1. $4\mu C$ and $8\mu C$ respectively
2. $8\mu C$ and $4\mu C$ respectively
3. $3\mu C$ and $6\mu C$ respectively
4. $6\mu C$ and $3\mu C$ respectively

Q. The wavelength of the first Balmer line caused by a transition from the $n=3$ level to the $n=2$ level in hydrogen is ${\lambda }_1$. The wavelength of the line caused by an electronic transition from $n=5$ to $n=3$ is$?$

1. $\frac{128}{375}{\lambda }_1$
2. $\frac{125}{64}{\lambda }_1$
3. $\frac{375}{128}{\lambda }_1$
4. $\frac{64}{125}{\lambda }_1$

Q. The Half life of a particle of mass $1.6\times {10}^{-26}$kg is $6.9$s and a stream of such particles is travelling with the K.E. of a particle being $0.05$eV. The fraction of particles which will decay when they travel a distance of $1$m is$?$

1. $0.1$
2. $0.01$
3. $0.0001$
4. $0.001$

Q. Two identical parallel plate capacitance C each are connected in series with a battery of emf, E as shown, If one of the capacitors is now filled with a dielectric of dielectric constant k, the amount of charge which will flow through the battery is $?$(neglect internal resistance of the battery)

1. $\frac{k+1}{2(k-1)}CE$
2. $\frac{k-1}{2(k+1)}CE$
3. $\frac{k-2}{k+2}CE$
4. $\frac{k+2}{k-2}CE$

Q. Consider the system shown. A horizontal force F is applied to a block X of mass $8$kg such that the block Y of mass $2$kg adjacent to it does not slip downwards under gravity. There is no friction between the horizontal plane and the base of the block X. The coefficient of friction between the surfaces of blocks X and Y is $0.5$. Take acceleration due to gravity to be $10m{s}^{-2}$. The minimum value of F is$?$

1. $40$N
2. $200N$
3. $240$N
4. $160$N

Q. A $160$watt light source is radiating light of wavelength $6200\stackrel{o}{A}$ uniformly in all directions. The photon flux at a distance of $1.8$m is of the order of (Plank's constant $6.63\times {10}^{-34}J-s$).

1. ${10}^{19}{m}^{-2}{s}^{-1}$
2. ${10}^2{m}^{-2}{s}^{-1}$
3. ${10}^{12}{m}^{-2}{s}^{-1}$
4. ${10}^{25}{m}^{-2}{s}^{-1}$

Q. An ideal gas follows a process described by $P{V}^2=C$ from $(P_1,V_1,T_1)$ to $(P_2,V_2,T_2)$ (C is a constant). Then.

1. If $P_1>P_2$ then $T_2>T_1$
2. If $V_2>V_1$ then $T_2<T_1$
3. If $V_2>V_1$ then $T_2>T_1$
4. If $P_1>P_2$ then $V_2>V_2$

Q. The maximum value attained by the tension in the string of a swinging pendulum is four times the minimum value it attains. There is no slack in the string. The angular amplitude of the pendulum is$?$

1. ${90}^o$
2. ${45}^o$
3. ${30}^o$
4. ${60}^o$

Q. A solid sphere spinning about a horizontal axis with an angular velocity $\omega$ is placed on a horizontal surface. Subsequently it rolls without slipping with an angular velocity of.

1. $2\omega /5$
2. $2\omega /7$
3. $7\omega /5$
4. $\omega$

Q. When ultraviolet radiation of a certain frequency falls on a potassium target, the photoelectrons released can be stopped completely by a retarding potential of $0.6$V. If the frequency of the radiation is increased by $10\%$, this stopping potential rises to $0.9$V. The work function of potassium is$?$

1. $2.4$eV
2. $2.0$eV
3. $3.0$eV
4. $2.8$eV

Q. The angle of incidence and refraction of a monochromatic ray of light of wavelength $\lambda$ at an air glass interface are i and r, respectively. A parallel beam of light with a small spread $\delta \lambda$ in wavelength about a mean wavelength $\lambda$ is refracted at the same air-glass interface. The refractive index $\mu$ of glass depends on the wavelength $\lambda$ as $\mu \left(\lambda \right)=a+b/{\lambda }^2$ where a and b are constant. Then the angular spread in the angle of refraction of the beam is$?$

1. $\left|\begin{array}{c}\frac{\sin i}{{\lambda }^3\cos r}\delta \lambda \end{array}\right|$
2. $\left|\begin{array}{c}\frac{2b}{{\lambda }^3}\delta \lambda \end{array}\right|$
3. $\left|\begin{array}{c}\frac{2b\tan r}{a{\lambda }^3+b\lambda }\delta \lambda \end{array}\right|$
4. $\left|\begin{array}{c}\frac{2b(a+b/{\lambda }^2)\sin i}{{\lambda }^3}\delta \lambda \end{array}\right|$

Q. One mole of a mono-atomic ideal gas is expanded by a process described by $P{V}^3=C$ where $C$ is a constant. The heat capacity of the gas during the process is given by ($R$ is the gas constant).

1. $2R$
2. $\frac{5}{2}$R
3. $\frac{3}{2}R$
4. $R$

Q. An electron enters a parallel plate capacitor with horizontal speed $\mu$ and is found to deflect by angle $\theta$ on leaving the capacitor as shown. It is found that $\tan \theta =0.4$ and gravity is negligible. If the initial horizontal speed is doubled, then $\tan$ will be.

1. $0.1$
2. $1.6$
3. $0.2$
4. $0.8$

Q. A simple pendulum is attached to block which slides without friction down an inclined plane(ABC) having an angle of inclination $\alpha$ as shown while the block is sliding down the pendulum oscillates in such a way that at its mean position the direction of the string is$?$

1. At angle $\alpha$ to the perpendicular to the inclined plane AC
2. Parallel to the inclined plane AC
3. Vertically downwards
4. Perpendicular to the inclined plane AC

Q. The binding energy per nucleon of ${}_5{B}^{10}$ is $8.0$MeV and that of ${}_5{B}^{11}$ is $7.5$MeV. The Energy required to remove a neutron from ${}_5{B}^{11}$ is (mass of electron and proton are $9.11\times {10}^{-31}$kg and $1.67\times {10}^{-27}$kg).

1. $8.0$MeV
2. $7.5$MeV
3. $0.5$MeV
4. $2.5$MeV

Q. Water containing air bubbles flows without turbulence through a horizontal pipe which has a region of narrow cross-section. In this region the bubbles.

1. Move with greater speed and are smaller than in the rest of the pipe
2. Move with greater speed and are larger in size than in the rest of the pipe
3. Move with lesser speed and are smaller than in the rest of the pipe
4. Move with lesser speed and are of the same size as in the rest of the pipe

Q. The dimensions of Stefan-Boltzmann constant $\sigma$ can be written in terms of Planck's constant $h$, Boltzmann constant $K_B$ and the speed of light $c$ as $\sigma =h^{\alpha }{K}_B$${}^{\beta }{c}^{\gamma }$. Here,

1. $\alpha =-3,\beta =4$ and $\gamma =-2$
2. $\alpha =3,\beta =4$ and $\gamma =-3$
3. $\alpha =2,\beta =-3$ and $\gamma =-1$
4. $\alpha =3,\beta =-4$ and $\gamma =2$

Q. Monochromatic light passes through a prism. Compares to that in air, inside the prism the light's.

1. Speed and wavelength are different but frequency remains same
2. Frequency and wavelength are different but speed remains same
3. Speed and frequency are different but wavelength remains same
4. Speed, wavelength and frequency are all different

Q. A solid expands upon heating because.

1. The potential energy of interaction between atoms in the solid is asymmetric about the equilibrium positions of atoms
2. The heating generates a thermal gradient between opposite sides
3. A fluid called the caloric flows into the interatomic spacing of the solid during heating thereby expanding it
4. The frequency of vibration of the atoms increases

Q. A solid cylinder P rolls without slipping from rest down an inclined plane attaining a speed $v_p$ at the bottom. Another smooth solid cylinder Q of same mass and dimensions slides without friction from rest down the inclined plane attaining a speed $v_q$ at the bottom. The ratio of the speeds $\left(\frac{v_p}{v_q}\right)$ is$?$

1. $\left(\sqrt{\frac{3}{4}}\right)$
2. $\left(\sqrt{\frac{3}{2}}\right)$
3. $\left(\sqrt{\frac{2}{3}}\right)$
4. $\left(\sqrt{\frac{4}{3}}\right)$

Q. A concave mirror of radius of curvature R has a circular outline of radius r. A circular disk is to be placed normal to the axis at the focus so that it collects all the light that is reflected from the mirror from a beam parallel to the axis. For $r<<R$, the area of this disc has to be at least.

1. $\frac{\pi r^6}{4R^4}$
2. $\frac{\pi r^4}{R^2}$
3. $\frac{\pi r^4}{4R^2}$
4. $\frac{\pi r^5}{4R^3}$

Q. A $1.5kW$ (kilo-watt) laser beam of wavelength $6400\mathring{A}$ is used to levitate a thin aluminium disc of same area as the cross section of the beam. The laser light is reflected by the aluminium disk without any absorption. The mass of the disc is close to:

1. ${10}^{-6}kg$
2. ${10}^{-3}kg$
3. ${10}^{-4}kg$
4. ${10}^{-9}kg$

Q. A uniform thin rod of length $2L$ and mass m lies on a horizontal table. A horizontal impulse J is given to the rod at one end. There is no friction. The total K.E. of the rod just after the impulse will be.

1. $J^2/2m$
2. $J^2/m$
3. $2J^2/m$
4. $6J^2/m$

Q. A certain p-n junction, having a depletion region of width $20\mu$m, was found to have a breakdown voltage of $100$V. If the width of the depletion region is reduced to $1\mu$m during its production, then it can be used as a zener diode for voltage regulation of.

1. $5$V
2. $10$V
3. $7.5$V
4. $2000$V

Q. The flat face of a plano-convex lens of focal length $10$cm is silvered. A point source placed $30$cm in front of the curved surface will produce a.

1. Real image $5$cm away from the lens
2. Real image $6$cm away from the lens
3. Virtual image $15$cm away from the lens
4. Virtual image $6$cm away from the lens

Q. Two identical metallic square loops $L_1$ and $L_2$ are placed next to each other with their sides parallel on a smooth horizontal table. Loop $L_1$ is fixed and a current which increases as a function of time is passes through it. Then loop $L_2$.

1. Rotates about its center of mass
2. Remains stationary
3. moves towards $L_1$
4. Moves away from $L_1$

Q. A whistle emitting a loud sound of frequency $540$Hz is whirled in a horizontal circle of radius $2$m and at a constant angular speed of $15rad/s$. The speed of sound is $330m/s$. The ratio of the highest to the lowest frequency heard by a listener standing at rest at a large distance from the center of the circle is$?$

1. $1.1$
2. $1.0$
3. $1.2$
4. $1.4$