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A circular coil of radius 4 cm and 20 turns carries a current of 3 ampere. It is placed in a magnetic field of 0.5 T. The magnitude of magnetic dipole moment of the coil will be?

A torch bulb rated as 4.5 W, 1.5 V is connected as shown in the figure. The e.m.f. of the cell needed to make the bulb glow at full intensity is

A cylindrical object of outer diameter 20 cm and mass the 2 kg floats in water with its axis vertical. If it is slightly depressed and then released, find the time period of the resulting simple harmonic motion of the object.

The horizontal range of an oblique projectile is equal to the distance through which a projectile has to fall freely from rest to acquire a velocity equal to the velocity of projection in magnitude. The angle of projection is

Two discs of radii $5\text{m}$ and $3\text{m}$ are joined together along their circumference as shown in the figure below. Find the centre of mass of the system of two discs

Consider the List I and List II

$\text{List~I}\text{P. Derivative control}\text{Q. Integral control}\text{R. Rate feed back control}\text{S. Proportional control}$

$\text{List~II}\text{1. Improved overshoot response}\text{2. Less steady state errors}\text{3. Less stable}\text{4. More damping}$

$\text{The correct match is}$

For plane electromagnetic waves propagating in the $z-$ direction, which one of the following combinations give the correct possible direction for $\overrightarrow{E}$ and $\overrightarrow{B}$ fields respectively?

Which of the following charge is not possible on a body?

(1) 1.6 x ${10}^{-18}$ C

(2) 1.6 x ${10}^{-20}$ C

(3) 1.6 x ${10}^{-14}$ C

(4) 1.6 x ${10}^{-5}$ C

In a sonometer wire, the tension is maintained by suspending a 50.7 kg mass from the free end of the wire. The suspended mass has a volume of $0.0075m^3$. The fundamental frequency of the wire is 260 Hz. If the suspended mass is completely submerged in water, the fundamental frequency will become

A point source $S$ emits light of wavelength $600\text{nm}.$ It is placed at a very small distance from a flat reflecting mirror $\text{AB}$. Interference fringes are observed on the screen placed parallel to the reflecting surface at very large distance $D$ from it. The ratio of minimum to maximum intensities in the interference fringes formed near the point $\text{P}$ is $\frac{1}{6}.$ If the ratio of intensity of the reflected light to the intensity of incident light is $0.09k.$ The value of $k$ is

A body of mass 0.5 kg is projected under gravity with a speed of 98 m/s at an angle of ${30}^{\circ }$ with the horizontal. The change in momentum (in magnitude) of the body is

A water treatment plant is required to process 28800 $m^3/d$ of raw water (density = $1000kg/m^3$), kinematic viscosity $={10}^{-6}{m}^2/s$. The rapid mixing tank imparts a velocity gradient of 900 $s^{-1}$ to blend 35 $mg/L$ of alum with the flow for a detention time of 2 min. The power input (W) required for rapid mixing is

Find the flux of the electric field through a spherical surface of radius R due to a charge of $10-7C$ at the centre and another equal charge at a point 2R away from the centre (figure 30-E2).the point P, the flux of the electric field through the closed surface

(a) will remain zero (b) will become positive

(c) will become negative (d) will become undefined .

Two moving coil meters,
M₁ and M₂ have the following particulars:

R₁ =
10 Ω, N₁ = 30,

A₁ =
3.6 × 10⁻³ m², B₁
= 0.25 T

R₂ =
14 Ω, N₂ = 42,

A₂ =
1.8 × 10⁻³ m², B₂
= 0.50 T

(The spring constants
are identical for the two meters).

Determine the ratio of
(a) current sensitivity and (b) voltage sensitivity of M₂
and M₁.

In an experiment on photoelectric effect, the emitter and the collector plates are placed at a separation of 10 $cm$ and are connected through an ammeter without any cell.



A magnetic field $B$ exist parallel to the plates. The work function of the emitter is 2.39 $eV$ and the light incident on it has wavelengths between 400 $nm$ and 600 $nm$ . Find the minimum value of $B$ for which the current registered by the ammeter is zero. Neglect any effect of space charge.

There is a hollow sphere of charge Q and radius R. The self-potential energy of the sphere is proportional to (charge)and (radius).

Four Charges $1\times {10}^{-8}C,-2\times {10}^{-8}C,3\times {10}^{-8},3\times {10}^{-8}$ are placed at the four corners of a square of side 1 m. The potential at the centre of the square is

A charge q, m enters a finite B - field with a speed v as shown (such that the charge enters the magnetic field region perpendicularly at a distance L from the top left corner in the figure). Find its deviation if $v=\frac{2qBL}{m}$

Explain why, the diffusion of a solid in another solid is a very slow process.

A cylinder of mass $M$, radius $R$ is resting on a horizontal platform (which is parallel to $xy-$plane) with its axis fixed along the $y-$axis and only free to rotate about its axis. The platform is given a motion in $x-$direction given by $x=A\cos \left(\omega t\right)$. There is no slipping between the cylinder and platform. The maximum torque acting on the cylinder during its motion is

Find the maximum angular displacement of the rod if a particle of mass $m$ moving with velocity $6\text{m/s}$ sticks to it after collision.

A conducting rod of $1\text{m}$ length is rotating with a frequency of $50\text{rev/s}$ inside the uniform magnetic field of $6.28\text{mT}$. The magnetic field is perpendicular to the plane of rotation.



Instead of rotating, if the rod moves with a speed of $v=6.28\text{m/s}$ in the plane perpendicular to the magnetic field, then the emf induced between the ends of the rod will be -



$v$ is perpendicular to the length of the rod.



​​​​​​​$[$1 Mark$]$

Terminal velocity of a spherical body of density ρ and radius r moving through a liquid of density ρ’ is given by