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A potential difference created between the two plates in the photoelectric experiment setup helps to accelerate the photoelectrons, so that all of them reach the collector plate and contribute to the current. In the absence of such an accelerating potential, will there be any photocurrent at all? (Assume the photoelectrons come out perpendicular to the emitter plate.)

The band gap in germanium is $\Delta E=0.68$$\text{eV}$. Assuming that the number of hole-electron pairs is proportional to $e^{\frac{-\Delta E}{2kT}}$, find the percentage increase in the number of charge carries in pure germanium as the temperature is increased from $300\text{K}$ to $320\text{K}$.

$(\text{Take}k=8.62\times {10}^{-5}{\text{eVK}}^{-1},e^{0.82}=2.27)$

The angular speed of a body changes from ${\omega }_1$ to ${\omega }_2$ due to changes in its moment of inertia without applying torque. The ratio of radius of gyration in the two cases is

Unit vector perpendicular to $x-y$ plane is

Consider $3^{rd}$ orbit of $H{e}^{+}$ (Helium), using non-relativistic approach, the speed of electron in this orbit will be [given $K=9\times {10}^9$ constant, Z = 2 and h(Planck’s Constant) = $6.6\times {10}^{-34}$ J s]

Light of wavelength $550\text{nm}$ passes through a narrow single slit of width $2.00\mu \text{m}$ and produces a diffraction pattern on the screen placed few meters away from the slit. Calculate the intensity relative to the central maximum at a point halfway between these two minima.



$\text{Take}:{\sin }^{-1}\left(0.275\right)={16}^{\circ }$

${\sin }^{-1}\left(0.550\right)={33.4}^{\circ },$

$\sin \left({24.7}^{\circ }\right)=0.417,$

$\sin \left(4.77\text{rad}\right)=-0.998$

From a tower of height $H$, a particle is thrown vertically upwards with a speed $u$. The time taken by the particle to hit the ground is $n$ times the time taken by it to reach the highest point of its path. The relation between $H$, $u$ and $n$ is

An aeroplane is flying horizontally with a velocity of 600 km/h at a height of 1960 m. When it is vertically above a point A on the ground, a bomb is released from it. The bomb strikes the ground at point B. The distance AB is

The smallest velocity (in $m/s$) with which a particle may be projected in order to have a range of $40m$ on the horizontal plane is
(Take $g=10m/s^2$)

A square hole of side length $l$ is made at a depth of $h$ and a circular hole of radius $r$ is made at a depth of $4h$ from the surface of water in a water tank kept on a horizontal surface. If $l<<h$, $r<<h$ and the rate of water flow from the holes is the same, then $r$ is equal to -

Light of wavelength $1824\stackrel{\circ }{A}$, incident on the surface of a metal, produces photo-electrons with maximum energy 5.3 eV. When light of wavelength $1216\stackrel{\circ }{A}$ is used, the maximum energy of photoelectrons is 8.7 eV. The work function of the metal surface is

Two bodies of masses ${}^{\prime }{m}^{\prime }$ and ${}^{\prime }4m^{\prime }$ are having linear momentum in the ratio of $2:1$, respectively. The ratio of their kinetic energy is

A wire of cross-sectional area A at temperature t is held taut with a negligible tension between two rigid supports. If the wire is cooled to a temperature $(t-\Delta t)$, what tension is developed in the wire? The coefficient of linear expansion is $\alpha$ and Young's modulus of the wire is Y.

Two wires are made of the same material and have the same volume. The first wire has a cross-sectional area $1{\text{mm}}^2$ and the second wire has cross-sectional area $4{\text{mm}}^2$. If the length of the first wire is increased by $\Delta L$ on applying a force of $10\text{N}$, how much force is needed to stretch the second wire by the same amount?

(a) Deduce the expression for the potential energy of a system of two charges $q_1$ and $q_2$ located $\overrightarrow{r}{}_1$ and $\overrightarrow{r}{}_2$ , respectively, in an external electric field.

(b) Three point charges, + Q + 2Q and – 3Q are placed at the vertices of an equilateral triangle ABC of side l. If these charges are displaced to the mid-point $A_1$, $B_1$ and $C_1$ ,respectively, find the amount of the work done in shifting the charges to the new locations.

OR

Define electric flux. Write its S.I unit.

State and explain Gauss’s law. Find out the outward flux to a point charge +q placed at the centre of a cube of side ‘a’. Why is it found to be independent of the size and shape of the surface enclosing it? Explain.

A $40\mu \text{F}$ capacitor in the defibrillator is charged to $3000\text{V}$. The energy stored in the capacitor is sent through a patient during a pulse of duration $2\text{ms}$. The power delivered to the patient is

An energy of $24.6\text{eV}$ is required to remove one of the electron from the ground state of a neutral helium atom. The energy $\left(\text{in eV}\right)$ required to remove both the electrons from the ground state of a neutral helium atom is:

1. 0.707

Eddy currents are produced when:

A solid, small ball supported by rope rotates in a circle of radius $r$. The ball follows circular motion with constant speed. Which of the following represents net force on ball?

A body of mass $1\text{kg}$ begins to move under the action of a time dependent force $\overrightarrow{F}=(2t\hat{i}+3t^2\hat{j})\text{N}$, where $\hat{i}$ and $\hat{j}$ are the unit vectors along the $x$ and $y$ axis. What power will be developed by the force at the time $t$ ?