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The two identical plates are given charges as shown in figure. If the plate area of either face of each plate is $A$ and separation between the plates is $d$, then find the amount of heat liberated after closing the switch.

How can we calculate potential difference between two points if we if we place cells and resistances between the two points.

A rectifier type AC voltmeter consists of a series resistance $R_s$ an ideal full-wave birdge rectifier and a PMMC instrument as shown in the figure. The internal resistance of the instrument is $100\Omega$ and a full scale deflection is produced by a DC current of 1 mA. The value of $R_s$. required to obtain full scale deflection with an AC voltage of 100 V(rms)applied of the input terminals is

A closely wound solenoid, $80\text{cm}$ long has $5$ layers of windings of $400$ turns each. The diameter of the solenoid is $1.8\text{cm}$. If the current carried is $8.0\text{A}$, estimate the magnitude of $B$ inside the solenoid near its centre.

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An alternating voltage of $260\text{V}$ and $\omega =500{\text{rad s}}^{-1}$ is applied in an series $\text{LCR}$ circuit, where $L=0.01\text{H},C=4\times {10}^{-4}\text{F}$ and $R=10\Omega$



$\left(ii\right)$ Find the power supplied by the source is- (in $\text{W}$)-

Find the time period of small oscillations of the following systems.

(p) A metre stick suspended through the 20 cm mark.

(q) A ring of mass m and radius r suspended through a point on its periphery.

(r) A uniform square plate of edge 'a' suspended through a corner.

(s) A uniform disc of mass m and radius r suspended through a point $\frac{r}{2}$ away from the centre.

(i)$2\pi \sqrt{\frac{2\sqrt{2}a}{3g}}$ (ii) 1.51 sec (iii) $2\pi \sqrt{\frac{3r}{3g}}$ (iv)$T=2\pi \sqrt{\frac{2R}{g}}$

An $L-R$ circuit is having $L=2.5\text{H}$, $R=1\Omega$ and $E=4\text{V}$ is switched on at $t=0.$ Find the power dissipated at $t=2.5\text{s}.$

Which of the following is NOT a property of an amorphous solid?

A unit vector along tangent to the curve $y=3x^2-2x+1$ at $(1,2),$ is

When forces $F_1,F_2,F_3$ are acting on a particle of mass m such that $F_{2}and{F}_3$ are mutually perpendicular, then the particle remains stationary. If the force $F_1$ is now removed then the acceleration of the particle is

Which of the following options look similar to the sum of the given 4 vectors ?

A closed rectangular tank is completely filled with water and is accelerated horizontally with an acceleration towards the right. Pressure is

$\left(i\right)$ maximum at, and $\left(ii\right)$ minimum at

A small object is projected up along the incline from point $A$ with speed $u.$ The incline surface has a coefficient of friction equal to $\frac{1}{\sqrt{3}}$. The particle returns after some time passing through point $\text{A}$ with speed $v$ down the incline. What is the value of $\frac{v}{u}$?

What comes next in the pattern given below?

Angle made by light ray with the normal in medium of refractive index $\sqrt{2}$ is

Suppose that a rigid body is free to rotate about a fixed point $O$. If a force $\overrightarrow{F}$ acts on the body at a point $P$, then the body will tend to rotate about an axis through $O$. This effect is measured by the torque vector $t$ which is given by $\overrightarrow{t}=\overrightarrow{r}\times \overrightarrow{F}$. Where $\overrightarrow{r}$ is the position vector$\overrightarrow{OP}=25\hat{i}$and$\overrightarrow{F}=10\hat{i}+10\sqrt{3}\hat{j}$. The straight line through $O$ determined by $\overrightarrow{t}$ is the axis of rotation. The vector $\overrightarrow{r},\overrightarrow{F}$ and $\overrightarrow{t}$ form a right handed system.

$\overrightarrow{t}$ is the torque, $\overrightarrow{F}$ is the force and $\overrightarrow{r}$ is the position vector, then $\left[\overrightarrow{t}\overrightarrow{r}\overrightarrow{F}\right]$ is equal to

In the adjoining ray-diagram are given the positions of an object $O$, image $I$ and two lenses $L_1$ and $L_2$. The focal length of $L_1$ is also given. Find the focal length of the lens $L_2$.

The temperature of gas is increased from $200\text{K}$ to $600\text{K}$ at a constant pressure. If initially the volume of gas is $10\text{cc}$, then the final volume of the gas will be (in $\text{cc}$)

Calculate the area of the parallelogram when adjacent sides are given by the vectors $\overrightarrow{A}=2\hat{i}+3\hat{j}+4\hat{k}$ and $\overrightarrow{B}=2\hat{i}-3\hat{j}+\hat{k}$

A body starts from rest at time $t=0$, the acceleration time graph is shown in the figure. The maximum velocity attained by the body will be

A wire of about 2 km can be drawn from a gram of gold. This is because of the property called ______.

A particle executes SHM, at what value of displacement are the kinetic and potential energies equal ?

The masses of 10 kg and 20 kg respectively are connected by a massless spring as shown in figure. A force of 200 N acts on the 20 kg mass. At the instant shown, the 10 kg mass has acceleration $12m/se{c}^2.$ What is the acceleration of 20 kg mass

A rocket has a mass of $1000\text{kg}$ with $50,000\text{kg}$ of fuel being stored on this rocket. The nozzle of the rocket lets out the exhaust gases at a speed of $500\text{m/s}$. If the rocket consumes fuel at the rate of $100\text{kg/s}$, what is the acceleration of the rocket after $5\text{minutes}$ in a gravity free space?

What is the condition after which on a two media interface total Internal Reflection will occur ?

The sound level at a point 5.0 m away from a point source is 40 dB. What will be the level at a point 50 m away from the source?

A charged particle of mass $m$ and charge $q$, moving under the influence of a uniform electric field $E\hat{i}$ and a uniform magnetic field $B\hat{k}$, follows a trajectory from point $P$ to $Q$ as shown in figure. The velocities at $P$ and $Q$ are respectively, $v\hat{i}\text{and}-2v\hat{j}$. Then, which of the following statements (A, B, C, D) are correct? (Trajectory shown is schematic and not to scale)





$\left(A\right)$ $E=\frac{3}{4}\left(\frac{m{v}^2}{qa}\right)$

$\left(B\right)$ Rate of work done by the electric field at $P$ is $\frac{3}{4}\left(\frac{m{v}^2}{a}\right)$.

$\left(C\right)$ Rate of work done by both the fields at $Q$ is zero.

$\left(D\right)$ The difference between the magnitude of angular momentum of the particle at $P$ and $Q$ is $2mav$.

The radius of curvature of a spherical mirror is $30\text{cm}$. What is its focal length if it always forms a virtual image?

Each of the resistors shown in figure (32-E11) has a resistance of 10 $\Omega$ and each of the batteries has an emf of 10 V. Find the currents through the resistors a and b in the two circuits.

In a YDSE arrangement separation between slits is d, screen is at distance D from the slits, and $\lambda$ is wavelength of light used.If intensity of light from each slit on the screen is $I_0$, then the minimum seperation between two lines on the screen, where intensity is $I_0$, is