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Figure 3.35 shows a 2.0
V potentiometer used for the determination of internal resistance of
a 1.5 V cell. The balance point of the cell in open circuit is 76.3
cm. When a resistor of 9.5 Ω is
used in the external circuit of the cell, the balance point shifts to
64.8 cm length of the potentiometer wire. Determine the internal
resistance of the cell.

A meter bridge setup as shown below is used to determine an unknown resistance $\text{X}$ using a standard $21\Omega$ resistor. If null point is at $40\text{cm}$ from $\text{A}$, and end correction at $\text{A, B}$ are $2.0\text{cm}$ each, find value of $\text{X}$,

The value of ${}^{\prime }{a}^{\prime }$ in Van der Waal's equation for the gases $O_2,N_2,N{H}_3$ and $C{H}_4$ are $1.35,1.38,4.16$ and $2.25$ respectively. The gas which can most easily be liquified is

Two small spheres each having the charge +Q are suspended by insulating threads of length L from a hook. This arrangement is taken in space where there is no gravitational effect, then the angle between the two suspensions and the tension in each will be

An iron rod of susceptibility $599$ is subjected to a magnetising field of $1200{\text{Am}}^{-1}$. The relative permeability of the material of the rod is

The absolute temperature of air in a region linearly increases from $T_1$ to $T_2$ in a space of width d. Find the time taken by a sound wave to go through the region in terms of $T_1,T_2,d$ and the speed v of sound at 273 K.

Two identical square rods of metal are welded end to end as shown in figure $\left(a\right)$, $20\text{calories}$ of heat flows through it in $4\text{minutes}$. If the rods are welded as shown in figure $\left(b\right)$, the same amount of heat will flow through the rods in

An
electron gun with its collector at a potential of 100 V fires out
electrons in a spherical bulb containing hydrogen gas at low pressure
(∼10⁻²
mm of Hg). A magnetic field of 2.83 × 10⁻⁴
T curves the path of the electrons in a circular orbit of radius 12.0
cm. (The path can be viewed because the gas ions in the path focus
the beam by attracting electrons, and emitting light by electron
capture; this method is known as the ‘fine beam tube’
method. Determine e/m
from the data.

In which one of the following pairs of experimental observations and phenomenon does the experimental observation correctly account for phenomenon

Experimental observation Phenomenon

Taking the electronic charge as ${}^{\prime }{e}^{\prime }$ and the permittivity as ${}^{\prime }{\epsilon }_0^{\prime }$, use dimenstional analysis to determine the correct expression for ${\omega }_p$

A
square loop of side 12 cm with its sides parallel to X and Y axes is
moved with a velocity of 8 cm s⁻¹
in the positive x-direction
in an environment containing a magnetic field in the positive
z-direction.
The field is neither uniform in space nor constant in time. It has a
gradient of 10⁻³
T cm⁻¹
along the negative x-direction
(that is it increases by 10^−
3 T cm⁻¹
as one moves in the negative x-direction),
and it is decreasing in time at the rate of 10⁻³
T s⁻¹.
Determine the direction and magnitude of the induced current in the
loop if its resistance is 4.50 mΩ.

A block A of mass 7 kg is placed on a frictionless table. A thread tied to it passes over a frictionless pulley and carries a body B of mass 3 kg at the other end. The acceleration of the system is $(giveng=10m{s}^{-2})$

If each capacitor has capacitance $C$ in the figure $\left(a\right)$ then find $C_{AB}$.

A uniform sphere of mass $M$ and radius $R$ exerts a force $F$ on a small mass $m$ situated at a distance of $2R$ from the centre $O$ of the sphere. A spherical portion of diameter $R$ is cut from the sphere as shown in the figure. The force of attraction between the remaining part of the sphere and the mass $m$ will be:

Find the equivalent capacitance of given circuit between points $\text{A}$ and $\text{B}$ ? (Take $C=12\mu \text{F})$

In the given circuit, the current through Zener diode is $\frac{5k}{3}\text{mA}$. The value of $k$ is

1. 31.98

A hemispherical tank of diameter 4m is filled with water. A very small hole is punched at 1m above the bottom as shown in figure. Find x (distance at which water strikes the surface)

A science student is riding on a flat car roof train travelling a straight horizontal track at a constant speed of 10 mps. The student throws a ball into the air along a path that he just to make an initial angle 60 degrees with the horizontal and to be in line with the track the student's professor who is standing on the ground nearby, observe the ball to rise. Vertically how high does the ball rise?

A juggler throws balls into the air. He throws one whenever the previous one is at its highest point. How high do the balls rise if he throws n balls in each second. Acceleration due to gravity is g.

A capacitor of capacitive reactance, $12\Omega$ is connected with an AC source having voltage, $V=3\sin (\omega t+\pi /6)$. Find the expression of instantaneous current in the circuit.

The dielectric strength of air is $3.0\times {10}^6\text{V/m}$. A parallel-plate air-capacitor has area $20{\text{cm}}^2$ and plate separation $0.10\text{mm}$. Find the maximum $rms$ voltage of an $\text{AC}$ source which can be safely connected to this capacitor.

The wavelength of the photoelectric threshold for silver is ${\lambda }_0$. The energy of the electron ejected from the surface of silver by an incident light of wavelength$\lambda (\lambda <{\lambda }_0)$ will be

A rectangular tank of depth 8 meter is full of water (), the bottom is seen at the depth [MP PMT 1987

Water flows in a horizontal tube. The pressure of water changes by 600 N m^-2between A and B where the areas of cross section are 30 cm² and 15 cm² respectively. Find the rate of flow of water through the tube. Given $\sqrt{0.4}$= 0.63 approx.

For a series LCR circuit, the power dissipated at resonance is (symbols have their usual meaning) ($I$ : rms current)

A long wire carrying a current i is bent to form a plane angle $\alpha$.Find the magnetic field B at a point on the bisector of this angle situated at a distance x from the vertex.

Four bodies A, B, C and D of masses $[M_A=m,M_B=2m,M_C=m,M_D=2m]$ are initially at rest. They start moving under the influence of the internal force of attraction and at a particular instant, their velocities are $V_A=2\hat{i},V_B=-\hat{i}+2\hat{j}$ and $V_C=-2\hat{i}+2\hat{j}$. Find the velocity of body D $\left(V_D\right)$ at that instant.

A uniformly charged ring of radius $3a$ and total charge $q$ is placed in $xy-$plane centred at origin. A point charge $q$ is moving towards the ring along the $z-$axis and has speed $v$ at $z=4a$. The minimum value of $v$ such that it crosses the origin is