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In space a uniform electric field exists in $x-$ direction. If the work done by external agent in moving a charge of $0.2\text{C}$ through a distance of $2\text{m}$ , slowly along the line making an angle of ${60}^{\circ }$ with $x-$ direction is $4\text{J}$, then the magnitude of the electric field $E$ is-

Two long straight wires carrying current of $5\text{A}$ each. Find the point for which magnetic field is zero

In a series of polaroids placed in such a way that the optical axis of each polaroid makes the same angle with the next one. When unpolarized light falls on first and if no light is coming out from the last polaroid, then by using how many number of polaroids in series this can be achieved?

A particle executes simple harmonic motion with an amplitude of 10 cm. At what distance from the mean position are the kinetic and potential energies equal?

Pressure of an ideal gas is obtained from kinetic gas equation. The kinetic gas equation is: $PV=\frac{1}{3}\left(m{N}_A\right)u^2=\frac{1}{3}M{u}^2$, where, $m{N}_A=M$(molar mass)

$N_A=\text{Avogadro's number}$

$u=\text{root mean square velocity}$

$\text{Translational kinetic energy of n mole}\frac{1}{2}M{u}^2=\frac{3}{2}\left(PV\right)=\frac{3}{2}\left(nRT\right)$

$\text{Average translational kinetic energy per molecule}=\frac{3}{2}\left(\frac{RT}{N_A}\right)=\frac{3}{2}\left(KT\right)$

$u_{rms}=\sqrt{\frac{3PV}{M}}=\sqrt{\frac{3RT}{M}}=\sqrt{\frac{3P}{d}}$

and $u_{av}=\sqrt{\frac{8RT}{\pi M}}$

The mass of molecule A is twice the mass of molecule B. The rms speed of A is twice the rms speed of B. If two samples A and B contain same number of molecules, what will be the ratio of pressures of 2 samples in 2 separate containers of equal volume?

A bomb at rest explodes into three equal fragments. Two fragments fly off at right angles with velocity $12\text{m/s}$ and $9\text{m/s}$. If the explosion process occurs in $0.1\text{s}$, find out the average force acting on the third particle, if total mass of the bomb is $12\text{kg}$.

1. 1

A smooth square platform ABCD is moving towards right with a uniform speed v. At what angle $\theta$ must a particle be projected from A with speed u so that it strikes the point B?

The maximum intensity in Young's double-slit experiment is $I_0$. The distance between the slits is $d=5\lambda$, where $\lambda$ is the wavelength of monochromatic light used in the experiment. What will be the intensity of light in front of one of the slits on a screen at a distance D = 10d?

A particle is moving such that its position coordinate $(x,y)$ are $(2\text{m},3\text{m})$ at time $t=0,$ $(6\text{m},7\text{m})$ at time $t=2\text{s}$ and

$(13\text{m},14\text{m})$ at time $t=5\text{s}$

Average velocity $\left({\overrightarrow{V}}_{av}\right)$ from $t=0$ to $t=5\text{s}$ is

In the arrangement shown in given figure current from A to B is increasing in magnitude. Induced current in the loop will

A wire of length $L$ and $3$ identical cells of negligible internal resistances are connected in series. Due to the current, the temperature of the wire is raised by $\Delta T$ in time $t$. $N$ number of similar cells are now connected in series with a wire of the same material and cross-section but of length $2L$. The temperature of the wire is raised by the same amount $\Delta T$ in the same time $t$. The value of $N$ is:

A charge $q$ is moving with a velocity $\overrightarrow{v_1}=\left(1\hat{i}\right)\text{m}/\text{s}$ at a point in a magnetic field and experiences a force $\overrightarrow{F_1}=q(-\hat{j}+\hat{k})$$\text{N}$. If the same charge is moving with a velocity $\overrightarrow{v_2}=\left(1\hat{j}\right)\text{m}/\text{s}$ at the same point, it experiences a force $\overrightarrow{F_2}=q(\hat{i}-\hat{k})\text{N}.$ The magnetic field $\overrightarrow{B}$ at that point is -

In the arrangement shown $\theta$ is varied between $0$ to $\frac{\pi }{2}.$ ( If $f_c:$ contact force, $N$ : normal Reaction, $f$ : friction), then which of the following variations are correctly shown

Two radioactive substances $A\text{and}B$ have decay constants $5\lambda \text{and}\lambda$ respectively. At $t=0$, a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to becomes ${\left(\frac{1}{e}\right)}^2$ will be

A block weighing 10 N travels down a smooth curved track AB joined to a rough horizontal surface (figure). The rough surface has a friction coefficient of 0.20 with the block. If the block starts slipping on the track from a point 1.0 m above the horizontal surface, how far will it move on the rough surface?

At what temperature will $H_2$ molecules have the same R.M.S velocity as $N_2$ molecules have at ${27}^{\circ }$C?

Ratio of longitudinal stress in case (I) & case (II) is
[Consider both wires are made of the same material]

A ball thrown by a boy is caught by another after 2 sec. some distance away in the same level. If the angle of projection is ${30}^{\circ }$, the velocity of projection is

In the figure shown, the static friction between all contact surfaces is $0.5$. What minimum force applied leftwards on block $1$ will move the system?

A large mass M moving with velocity v makes an elastic head-on collision with a small mass m at rest. What will be the expression for energy lost by mass M?