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The cube shown in the figure has sides of length $L=10.0\text{cm}$. The electric field is uniform, has a magnitude $E=4.00\times {10}^{-3}{\text{NC}}^{-1}$ and is parallel to the $xy$ plane at an angle of ${37}^{\circ }$ measured from the $+x$-axis toward the $+y$-axis.

Given $\sin {37}^{\circ }=0.6$, $\cos {37}^{\circ }=0.8$



$\left(ii\right)$ Electric flux passing through surface $S_1$ is



​​​​​​​$[$1 Mark$]$

A force of 20 N is applied on a body of mass 4 kg kept on a rough surface having coefficient of friction 0.1. Find acceleration of body. Take g = 10 m/s²

Difference in height between the liquid columns in the vertical arms is - [Take $g=10{\text{m/s}}^2$]

According to Bohr's theory, the energy of an electron in the $n^{th}$ orbit of an atom of atomic number Z is proportional to

When two capillary tubes of different diameters are dipped vertically, the rise of the liquid is

Find the voltage drop across a capacitor connected with a resistance and a battery of $60\text{V}$ in series, after a long time:-

The two particles of equal mass $\text{m}$ go round a circle of radius $\text{R}$ under the action of their mutual gravitational attraction. The speed of each particle is :

Four identical thin rods each of mass M and length l, from a squre frame. Moment of inertia of this frame about an axis through the centre of the square and perpendicular to its plane is

The intensity of solar radiation incident at the level of upper atmosphere of the earth is $1.35{\text{kW/m}}^2$. What is the force exerted by this radiation on the solar panel of a satellite, of area $100{\text{m}}^2$. Assume normal incidence and complete absorption.

A light spring of force constant $K$ is held between two blocks of masses $m$ and $2m$. The two blocks and the spring system rests on a smooth horizontal floor. Now the blocks are moved towards each other compressing the spring by $x$ and then they are suddenly released. Then find the relative velocity between the blocks when the spring attains its natural length.

In a bicycle competition called Tour De France, two riders; $A$ and $B$ are riding bicycles at constant acceleration of magnitude $1{\text{m/s}}^2$ and $3{\text{m/s}}^2$ respectively, in the North direction. Their initial speeds are $15\text{m/s}$ and $10\text{m/s}$ respectively while they were heading in the North direction. Find the separation between them after $t=10\text{s}$.

A body moves over one-fourth of a circular arc in a circle of radius $r$. The magnitude of distance travelled and displacement will be respectively

The magnetic field inside a long solenoid is increased from $2\times {10}^{-3}\text{T}$ to $2.5\text{T}$ when an iron core is inserted in it. Find the relative permeability of the iron core.

A rigid body of mass 'm' and radius 'r' rolls without slipping on a rough horizontal surface. A force is acting on a point 'x' distance from the center as shown in figure. Assuming the moment of inertia of the solid body about an axis through its COM be $I_{CM}$. Find the value of x so that static friction is zero.

A particle is moved along a path $AB-BC-CD-DE-EF-FA$, as shown in figure in presence of a force $\overrightarrow{F}=(\alpha y\hat{i}+2\alpha x\hat{j})N$, where x and y are in meter and $\alpha =-1N{m}^{-1}$. The work done on the particle by this force $\overrightarrow{F}$ will bejoule. (write up to two decimal places)

Two satellites $\text{A}$ and $\text{B}$ go round a planet $\text{P}$ in circular orbits having radii $4R$ and $R$ respectively. If the speed of the satellite $\text{A}$ is $3v$, the speed of the satellite $\text{B}$ will be

A rod of mass $m$ is placed on two supports as shown. Calculate the normal reaction of each support.

One mole of helium is kept in a cylinder of cross-section $A=8.5{\text{cm}}^2$. The cylinder is closed by a light frictionless piston. The gas is slowly heated in a process during which a total of $42\text{J}$ heat is given to the gas. If the temperature rises through $2^{\circ }C$, find the displacement of the piston.

Atmospheric pressure $=100\text{kPa.}$

The internal energy of $n$ moles of a monoatomic ideal gas is $1.5\text{nRT}$.

A block of mass $m$ is suspended by different springs of force constant shown in figure.

Let time period of oscillation in these four position be $T_1,T_2,T_{3}and{T}_4$. Then,

(Consider springs to be massless.)

An elastic circular wire of length l carries a current I. It is placed in a uniform magnetic field $\overrightarrow{B}$ (Out of paper) such that its plane is perpendicular to the direction of $\overrightarrow{B}$. The wire will experience

The acceleration of a particle is increasing linearly with time t as bt . The particle starts from the origin with an initial velocity $v_o$. The distance travelled by the particle in time t will be

What is the current in the circuit given below?

A coil of area $10{\text{cm}}^2$ has $200$ turns. Magnetic field of $0.1{\text{Wb/m}}^2$ is perpendicular to the plane of the coil. The field is reduced to zero in $0.1\text{s}$, the induced emf in the coil is



​​​​​​​$[$1 Mark$]$

An alternating current is given by the equation, $i=i_1\sin \omega t+i_2\cos \omega t$. The RMS value of current will be :

Find the angle of incidence so that the incident light ray retraces its path after third reflection.