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A scale which is calibrated at ${10}^{\circ }\text{C}$ measures the length of a stick to be $60\text{cm}$, at temperature ${30}^{\circ }\text{C}$ . If thermal coefficient of linear expansion of the rod is $2\times {10}^{-5}{/}^{\circ }\text{C}$, the correct length of the stick in $\text{cm}$ is:

Following figure shows an adiabatic cylindrical container of volume $V_o$ divided by an adiabatic smooth piston (area of cross section = $A$) in two equal parts. An ideal gas $(\frac{C_P}{C_V}=\gamma )$ is at pressure $P_1$ and temperature $T_1$ in left part and gas at pressure $P_2$ and temperature $T_2$ in right part. The piston is slowly displaced and released at a position where it can stay in equilibrium. The final pressure of the two parts can be (Suppose $x$ is displacement of the piston)

The velocity-time graph of a particle in straight-line motion is shown in the figure. The particle starts its motion from the origin.



The displacement of the particle in $8s$ is

Electric charge is uniformly distributed along a long straight wire of radius 1 mm. The charge per cm length of the wire is Q coulomb . Another cylindrical surface of radius 50 cm and length 1 m symmetrically encloses the wire as shown in the figure. The total electric flux passing through the cylindrical surface is

All bulbs consume same power. The resistance of bulb $1$ is $36\Omega$.





$\left(i\right)$ What is the resistance of bulb $3?$

A $70\text{kg}$ man stands in contact against the inner wall of a hollow cylindrical drum of radius $3\text{m}$ rotating about its vertical axis. The coefficient of friction between the wall and his clothing is $0.15$. What is the minimum rotational speed of the cylinder to enable the man to remain stuck to the wall (without falling) when the floor is suddenly removed?

Two light springs of force constant $K_1$ and $K_2$ and a block of mass $m$ are arranged in one line $AB$ on a smooth horizontal table such that one end of each spring is fixed on rigid supports and the other end is free as shown in the figure. The distance $CD$ between the free ends of the spring is $60\text{cm}$. If the block moves along $AB$ with a velocity $120\text{cm/s}$ in between the springs, calculate the period of oscillation of the block.
$(K_1=1.8\text{N/m},K_2=3.2\text{N/m},m=200\text{gm})$

A radioactive element emits 200 particles per second. After three hours 25 particles per second are emitted. The half-life period of element will be

A block with a mass of $3\text{kg}$ is suspended from an ideal spring having negligible mass which stretches the spring by $0.2\text{m}$ at equilibrium. Find the force constant of the spring.

Some physical quantities are given in Column I and some possible SI units in which these quantities may be expressed are given in Column II. Match the physical quantities in Column I with the units in Column II.
$\begin{array}{cccc}& \text{Column I}& & \text{Column II}\\ i& G{M}_e{M}_S& \text{a.}& \left(kg\right)\left(metre{)}^2\right(second{)}^{-2}\\ ii& 3RT& \text{b.}& \left(farad\right)\left(volt{)}^2\right(kg{)}^{-1}\\ iii& F^2/q^2{B}^2& \text{c.}& \left(volt\right)\left(coulomb\right)\left(metre\right)\end{array}$

Where G is universal gravitational constant; $M_e$= mass of the earth; $M_s$= mass of sun; $R$ = universal gas constant; $T$ = absolute temperature; $F$ = force; $q$ = charge; $B$ = magnetic field $\left(M{A}^{-1}{T}^{-2}\right)$. $(1\text{volt}=\frac{1\text{joule}}{1\text{coulomb}};1\text{farad}=\frac{1\text{coulomb}}{1\text{volt}})$

The potential energy for a force field $\overrightarrow{F}$ is given by $U(x,y)=\cos (x+y)$. The force acting on a particle at the position given by coordinates $(0,\frac{\pi }{4})$ is

A siren placed at a railway platform is emitting a sound of frequency $5\text{kHz}$. A passenger sitting in a moving train $\text{A}$ records a frequency of $5.5\text{kHz}$ when the train approaches the siren. During his return journey in a different train $\text{B}$ he records a frequency of $6.0\text{kHz}$ while approaching the same siren. The ratio of velocity of train $\text{B}$ to that of train $\text{A}$ is

A vessel of depth 2d cm is half filled with a liquid of refractive index ${\mu }_1$ and the upper half with a liquid of refractive index ${\mu }_2$. The apparent depth of the vessel seen perpendicularly is

The magnitude of force due to an electric dipole of dipole moment $3.6\times {10}^{-29}\text{C-m}$ on an electron $25\text{nm}$ from the centre of the dipole along the dipole axis is

A long solenoid has $800$ turns per metre length of solenoid. A current of $1.6\text{A}$ flows through it.



$\left(i\right)$ Find the value of magnetic field at the end of the solenoid on its axis.



​​​​​​​$[$1 Mark$]$

At a certain place the angle of dip is ${30}^{\circ }$ and the horizontal component of earth's magnetic field is $0.50\text{Oe}$. The earth's total magnetic field is (in Oestred)

A semicircular wire of radius 5.0 cm carries a current of 5.0 A. A magnetic field B of magnitude 0.50 T exists along the perpendicular to the plane of the wire. Find the magnitude of the magnetic force acting on the wire.

Two toroids $\text{A}$ and $\text{B}$ have the total number of turns $3n$ and $n$ respectively with average radii $r$ and $3r$ respectively. If the both toroids carries equal amounts of current, the ratio of magnetic field inside the core of toroids is

Explain the reason behind the animals falling during rain? Please give clear explain.

A
modulating signal is a square wave, as shown in Fig. 15.14.

The
carrier wave is given by

(i)
Sketch the amplitude modulated waveform

(ii)
What is the modulation index?

We understand 'temperature' as a measure of the 'hotness' or 'coldness' of a body. Which of these properties do you think explicitly depend on the temperature?

The
magnetic moment vectors μ_sand μ_lassociated with the intrinsic spin
angular momentum S and
orbital angular momentum l,
respectively, of an electron are predicted by quantum theory (and
verified experimentally to a high accuracy) to be given by:

μ_s= –(e/m)
S,

μ_l
= –(e/2m)l

Which
of these relations is in accordance with the result expected
classically?
Outline the derivation of the classical result.

A smooth wire of length $2\pi r$ is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed $\omega$ about the vertical diameter $\text{AB}$, as shown in figure, the bead is at rest with respect to the circular ring, at position $P$, as shown. Then the value of ${\omega }^2$ is equal to :

1. 82

Do
the same exercise as above with the replacement of the earlier
transformer by a 40,000-220 V step-down transformer (Neglect, as
before, leakage losses though this may not be a good assumption any
longer because of the very high voltage transmission involved).
Hence, explain why high voltage transmission is preferred?

A uniform metallic disc of radius r and mass m is spinning with angular speed ${\omega }_0$ about an axis passing through its centre and perpendicular to its plane. If its temperature is increased (slightly) by $\Delta T$ without disturbing the disc, its new angular speed is (The coefficient of linear expansion of the metal is $\alpha$ )

Let a continuous time signal be defined as $g\left(t\right)=rect\left(4t\right)\ast 4\delta (-2t)$ then the Fourier transform of the signal g(f) is given as



(where $sinc\left(f\right)=\frac{sin\pi f}{\pi f}$)

A $2.0\text{kg}$ block is dropped from a height of $40\text{cm}$ onto a spring of spring consant $k=1960\text{N/m}$. Find the maximum distance the spring is compressed.