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Two infinitely long current carrying wires are separeted by $5\text{m}$ lying parallel to each other if current through the first wire is $2.5\text{A}$ upwards then what is the current in the 2nd wire so that magnetic field at the mid point between them is $\frac{{\mu }_0}{4\pi }$ out of the plane of paper-

Comprehension :



A $100\Omega$ resistance is connected in series with a $4\text{H}$ inductor. The voltage across the resistor is, $V_R=2.0\sin \left({10}^{3}t\right)\text{V}.$



$\left(i\right)$ Find the expression of circuit current-

A parallel plate capacitor consists of two plates, each with area $A$ and separated by a distance $d$. What will be the work done against electrostatic force in increasing the separation between the plates from $l_1$ to $l_2$, while the potential difference $V$ across the capacitor is kept constant ?

A body of mass m rises to height $h=\frac{R}{5}$ from the earth's surface, where R is earth's radius. If g is acceleration due to gravity at earth's surface, the increase in potential energy is

A cubical metal block of edge $12\text{cm}$ floats in mercury with one fifth of the height inside the mercury. Water is poured till the surface of the block is immersed in it. Height of the water column to be poured is [specific gravity of mercury$=13.6$]

Find the flux through the surface $\left(APB\right)$ of the given Gaussian surface containing a point charge $+9\text{nC}$ as shown in figure.

[$ABC$ is an equilateral triangle and take ${ϵ}_o=9\times {10}^{-12}{\text{C}}^2/{\text{N-m}}^2$]

The correct value of dip angle at a place is ${45}^{\circ }$. If the dip circle is rotated by ${45}^{\circ }$ out of the meridian, then the tangent of the angle of apparent dip at the place is

A particle of mass $M$ is placed at the centre of a uniform spherical shell of equal mass and radius $a$. Find the gravitational potential at a point $\text{P}$ at a distance $a/2$ from the centre.

Current in a coil increases from 0 to 1 ampere in 0.1 second. If self inductance of the coil is 5 millihenry, magnitude of induced emf is

Two blocks $A$ and $B$ of equal mass $m=1.0\text{kg}$ are lying on a smooth horizontal surface as shown in figure. A spring of force constant $k=200\text{N/m}$ is fixed at one end of block $A$. Block $B$ collides with block $A$ with velocity $v_0=2.0\text{m/s}$. Find the maximum compression of the spring.

Three vectors $\overrightarrow{A},\overrightarrow{B}\&\overrightarrow{C}$ are given as $\overrightarrow{A}=2\hat{i}+3\hat{j}+4\hat{k},\overrightarrow{B}=\hat{i}+2\hat{j}+2\hat{k}$ and $\overrightarrow{C}=m\hat{i}+2\hat{j}+\hat{k}$. Find the value of $m$, for which these vectors are coplanar.

1. 200

If $\overrightarrow{A}=3\hat{i}+6\hat{j}and\overrightarrow{B}=\hat{i}+4\hat{j}$ , what angle does ($\overrightarrow{A}-\overrightarrow{B}$ ) make with positive x-axis?

A uniform disc of mass 500 kg and radius 2 m is rotating at the rate of 600 r.p.m. What is the torque required to rotate the disc in the opposite direction with the same angular speed in a time of 100 second ?

A wave is travelling on a string with velocity $V_0$. If the mass of the string is doubled and length is tripled, what is the new velocity for the given Tension in the string?

A cylinder rotating at an angular speed of $50\text{rev/s}$ is brought in contact with an identical stationary cylinder. Because of the kinetic friction, torque acts on the both the cylinders, accelerating the stationary one and decelerating the moving one. If the common magnitude of the acceleration and deceleration be one revolution per second square, how long will it take before the two cylinders have equal angular speed ?

For a particle moving along circular path, the radial acceleration $a_r$ is proportional to time $t$. If $a_t$ is the tangential acceleration, then which of the following will be independent of time?

A body of mass $1kg$ is traveling with a velocity of $3m/s$ accelerates uniformly to acquire a velocity of $8m/s$ in $2s$. Find the force acting on the body.

The position vector of three particles of masses $m_1=1\text{kg},m_2=2\text{kg}$ and $m_3=3\text{kg}$ are ${\overrightarrow{r}}_1=(\hat{i}+4\hat{j}+\hat{k})\text{m},{\overrightarrow{r}}_2=(\hat{i}+\hat{j}+\hat{k})\text{m}$ and ${\overrightarrow{r}}_3=(2\hat{i}-\hat{j}-2\hat{k})\text{m}$ respectively. The position vector of their centre of mass is

A smooth sphere of mass $M$ moving with velocity $u$ directly collides elastically with another sphere of mass $m$ at rest. After the collision, their final velocities are $V$ and $v$ respectively. The value of $v$ is:

A body starts from rest and is accelerated by a force $F=kt\left(\text{N}\right)$. Options given below show the variation of power with time. Find the correct option related to the above case.

A long straight wire carries a current $I$. A particle at point $P$ having a positive charge $q$ and mass $m$, kept at a distance $x_o$ from the wire, is projected towards it with a speed $v$ as shown in the diagram. Find the minimum separation between the wire and the particle.



$($Magnetic field due to wire is $\overrightarrow{B})$

Find equivalent resistance between A and B

A particle is released from a height H and at certain height its kinetic energy is two times its potential energy, then the height and speed of the particle at that instant are

A mild steel wire of length 1.0 m and cross-sectional area
0.50 × 10^–2 cm² is stretched,
well within its elastic limit, horizontally between two
pillars. A mass of 100 g is suspended from the mid-point of the wire.
Calculate the depression at the midpoint.

A metre stick is held vertically with one end on a rough horizontal floor. It is gently allowed to fall on the floor. Assuming that the end at the floor does not slip, find the angular speed of the rod when it hits the floor

A container has a small hole at its bottom. Area of cross-section of the hole is $A_1$ and that of the container is $A_2.$ Liquid is poured into the container at a constant rate of $Q\text{m}{}^3\text{/s}.$ The maximum level of liquid in the container will be -

A uniform electric field of $100\text{V/m}$ is directed at ${30}^{\circ }$ with the positive $\text{x-}$axis as shown in figure. Find the potential difference $V_{BA}$ if $\text{OA}=2\text{m}$ and $\text{OB}=4\text{m}$.

Two identical flutes produce fundamental notes of frequency 300 Hz at ${27}^0$C. If the temperature of air in one flute is increased to ${31}^0$C, the number of the beats heard per second will be

The kinetic energies of a planet in an elliptical orbit about the Sun, at positions $\text{A, B}$ and $\text{C}$ are $K_A$, $K_B$ and $K_C$, respectively. $\text{AC}$ is the major axis and $\text{SB}$ is perpendicular to $\text{AC}$ at the position of the Sun $S$ as shown in the figure. Then