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In the FET amplifier circuit shown in figure ,the signal outputs $V_1$ and $V_2$ are related as

If fish are flowing at a rate of 10 fish/$m^{2}s$, and the 10 $m^2$ net is dipped at an angle of ${60}^0$ in their path for 1 second, how many fish do we catch?

A uniform constant magnetic field $\overrightarrow{B}$ is directed at an angle of ${45}^{\circ }$ to the $\text{x-axis}$ in the $\text{x-y}$ plane. $\text{PQRS}$ is a rigid, square wire frame carrying a steady current $I_o\left(\text{anticlockwise}\right)$, with its centre at origin $O$. At time $t=0$, the frame is at rest in the position shown in the figure with its sides parallel to the $x$ and $y$ axes. Each side of the frame is of mass $M$ and length $L$.



Find the angle by which the frame rotates under the action of this torque in a short interval of time $\Delta t$. $(\Delta t$ is short, so that any variation in the torque during this interval may be neglected$)$.



Given: The moment of inertia of the frame about an axis through its centre perpendicular to its plane is $\frac{4}{3}M{L}^2$.

A parallel plate capacitor with the plate area $100{\text{cm}}^2$ and the separation between the plates $1.0\text{cm}$ is connected across a battery of emf $24\text{V}$. Find the force of attraction between the plates.

The circuit below is made up using identical light bulbs. The light bulb of maximum brightness among the following will be

The potential energy of a certain particle is given by $U=\frac{1}{2}(x^2-y^2)$. The force on it is:

A ball of ice which is at $-20{}^{\circ }\text{C}$ temperature falls into a tub full of water which is at $52{}^{\circ }\text{C}$ temperature. Calculate the mass of ice, if mass of water in tub is $500\text{gm}$ and final temperature of mixture is $48{}^{\circ }\text{C}$.

Given : $S_{ice}=0.5{\text{cal/gm}}^{\circ }\text{C}$, $S_{water}=1{\text{cal/gm}}^{\circ }\text{C};L_{ice}=80\text{cal/gm}$

Why does there have to be an electric field if there is a potential difference?

Boyle's, Charles' and Avogadro's results on the different state variables of a gas, can be combined into one "equation of state” known as the ideal gas equation, PV = nRT, where R = 8.514 J/mol-K. Consider the following situation.

A mixture of hydrogen and oxygen has volume $2000c{m}^3$, temperature 300 K, pressure 100 kPa and mass 0.76 gms. Calculate the masses of hydrogen and oxygen in the mixture.

The ideal gas law, which relates the P, V and temperature T of an ideal gas in a closed box, given as PV = nRT, can be manipulated to construct an effective thermometer. A "constant volume gas thermometer” uses a sample of gas (commonly, nitrogen or helium) in a closed chamber, thus fixing the volume V. The temperature is then measured by reading off the corresponding pressure P. At the freezing point of water, it is seen that a gas thermometer records a pressure of 0.9 x 10⁵ Pa; it also records a pressure of 1.2 x 10⁵ Pa at the boiling point of water. What pressure will you find in the gas chamber at a room temperature of 23⁰C?

A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of impact with the bottom of the well. The error in his measurement of time is $\delta T=0.01$ seconds and he measures the depth of the well to be $L=20$ meters. Take the acceleration due to gravity $g=10m{s}^{-2}$ and the velocity of sound is $300m{s}^{-1}$. Then the fractional error in the measurement, $\delta L/L$, is closest to

Identify the incorrect displacement-time curve which does not represent motion in one dimension.

A circular disc of mass ${}^{\prime }2m^{\prime }$ and radius ${}^{\prime }{R}^{\prime }$, is hinged at centre. A long string is wound over this disc and a body of mass ${}^{\prime }{m}^{\prime }$ is attached at its free end. Now the body is released. Find acceleration of this body.

A car moves with a speed of 54 km $h^{-1}$ towards a cliff. The horn of the car emits sound of frequency 400 Hz at a speed of 335 m $s^{-1}$. (a) Find the wavelength of the sound emitted by the horn in front of the car. (b) Find the wavelength of the wave reflected from the cliff. (c) What frequency does a person sitting in the car hear for the reflected sound wave ? (d) How many beats does he hear in 10 seconds between the sound coming directly from the horn and that coming after the reflection ?

A transverse wave $y=5\sin (3t-x)$, where $y,x,t$ are in SI units, is propagating on a stretched string having density $\rho =1{\text{kg/m}}^3$. Find the intensity of the propagating wave.

If velocity (V), force(F) and time(t) are taken to be fundamental quantities and K is the dimensionless constant of proportionality, find the dimensional formula for mass.

Radition from hydrogen discharge tube falls on a cesium plate. Find the maximum possible kinetic energy of the photoelectrons. Work function of cesium is 1.9 e V.

Resistance of a resistor at temperature $t$ ${}^o\text{C}$ is $R_t=R_0(1+\alpha t+\beta t^2)$, where $R_0$ is the resistance at $0{}^o\text{C}$. The temperature coefficient of resistance at temperature $t{}^o\text{C}$ is

In my earlier question"s answer.. . I am not able to see full picture pastet and some words on right side are also cut

The number of stator teeth in a variable reluctance stepper motor is 16. And, the number of rotor teeth is 8. Calculate the stepping angle of the motor

An inclined tube manometer has a well of 20 mm in diameter and a tube of 4 mm of inner bore. If it is proposed to use a scale graduated accurately in mm to measure the pressure directly i.e. 1 mm scale division indicates a 1 mm pressure head change, then the angle at which the tube must be inclined with respect to vertical to do this is close to



$(\text{Density of mercury is}13.56\times {10}^{3}kg/m^3,1mmofHg=133N/m^2$

A capacitor of capacitance $1\mu \text{F}$ is discharging through a resistance. Initially, the potential difference across the capacitor is $12\text{V}$. At $t=\frac{1}{10}\text{sec}$, potential difference across capacitor becomes $6\text{V}$. Find the value of resistance $R$.

[Take $\ln 2=0.693$]

Four point masses, each of mass $m$ are fixed at the corners of a square of side $l$. The square is rotating with angular frequency $\omega$, about an axis passing through one of the corners of the square and parallel to its diagonal, as shown in the figure. The angular momentum of the square about this axis is:

A steel rod of $10\text{mm}$ diameter is loaded with a force of $20\text{kN}$. Change in diameter of the rod is $3.82\times {10}^{-3}\text{mm}$ . Given, Young's modulus for steel is $200\text{GPa}$, find its Poisson's ratio.

A ball drops from the ceiling of the room, and after rebounding twice from the floor, reaches a height equal to half that of ceiling. Find the coefficient of restitution?

Ship $A$ is travelling with a velocity of $5{\text{km h}}^{-1}$ due east. The second ship is heading ${30}^{\circ }$ east of north. What should be the speed of second ship if it is to always remain due north with respect to the first ship?

A punching press punches 30 holes per min in a plate requiring 12 kJ of energy per hole during each cycle. Actual punching takes 30% of the cycle time. A flywheel connected to the machine electric motor. The flywheel rotates at a mean speed of 240 rpm and the fluctuation of speed is not to exceed $\pm$ 2 percent of the mean speed

The moment of inertia of the fly wheel lo be used is

The international space station is maintained in a nearly circular orbit with a mean altitude of 330 km and a maximum of 410 km. An astronaut is floating in the space station’s cabin. The acceleration of astronaut as measured from the earth is.

^{x² = 1 + t² . Find the acceleration. Where x is displacement and t is time.}

two balls A and B are thrown simultaneously vertically upwards with a speed of 20 metre per second from the ground and the downwards s from a height of 40m with the same speed and along the same line of motion at what point does the ball collide?

In the figure shown, for the given values of $R_1\text{and}{R}_2$, the balance point for jockey is at $40\text{cm}$ from A. When $R_2$ is shunted by a resistance of $10\Omega$, the balance point shifts to $50\text{cm}$. If the length of AB is $1\text{m}$, the values of $R_1\text{and}{R}_2$ are

A pulse is travelling on string is described by $y=\frac{8}{(7x+24t{)}^2+16}$. What is the velocity of pulse?