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When a ceiling fan is switched on it starts from rest, while completing the $5^{th}$ rotation it has angular velocity of $20\text{rad/s}$, what will be the angular velocity of the fan while completing the ${15}^{th}$ rotation ? (Assume uniform angular acceleration)

Value of spring constant depends upon

Coherent sources are characterized by the same

[KCET 1993]

A slab of glass of thickness of $3$ units and refractive index $\sqrt{3}$ is surrounded by vacuum and is placed as shown. A light ray is incident at the point $(2,5\sqrt{3})$ as shown. The point where the ray will cut the $X-$ axis is:

The heats of combustion of $C_x{H}_y$, carbon and hydrogen are a, b and c $cal$ respectively. The heat of formation of $C_x{H}_y$ will be:

An ideal gas having density $1.7\times {10}^{-3}gc{m}^{-3}$ at a pressure $1.5\times {10}^5$ Pa is filled in a Kundt tube. When the gas is resonated at a frequency of 3.0 kHz, nodes are formed at a separation of 6.0 cm. Calculate the molar heat capaticies $C_p$ and $C_v$ of the gas.

A potential difference is set up between the plates of a parallel plate capacitor by a battery and then the battery is removed. If the distance between the plates is decreased, then how the (a) charge (b) potential difference (c) electric field (d) energy and (e) energy density will change?

when a body is at motion then which friction froce is acted upon the body and why?

Three infinite long plane sheets carrying uniform charge densities
${\sigma }_1=-\sigma ,{\sigma }_2=+2\sigma$ and ${\sigma }_3=+3\sigma$ are placed parallel to the x-z plane at y =a, y=3a and y=4a as shown in Fig. 20.18. The electric field at point P is

When liquid gas is released from a pressurized container why does the container gets too cold

$Ifsinx+si{n}^{2}x+si{n}^{3}x=1,thenco{s}^{6}x-4co{s}^{4}x+8co{s}^{2}xisequalto$

Match the following with regard to ECG
$\begin{array}{cc}\text{1.P-wave}& \text{A.Depolarization~of~inter~ventricular~septum}\\ \text{2.Q-wave}& \text{B.Rapid~ventricular~depolarization}\\ \text{3.T-wave}& \text{C.Ventricular~repolarization}\\ \text{4.QRS~complex}& \text{D.~Atrial~depolarization}\end{array}$

If a small sphere of mass m and charge q is hung from a silk thread at an angle $\theta$ with the surface of a vertical charged conducting plate, then for equilibrium of sphere, the surface charge density of the plate is

If $\overrightarrow{V_r}$ is the velocity of rain falling vertically and $\overrightarrow{V_m}$ is the velocity of a man walking on a level road, and $\theta$ is the angle with vertical at which he should hold the umbrella to protect himself, then the magnitude of relative velocity of rain w.r.t man is given by

The coefficient of static friction is 0.800 between the
soles of a sprinter’s running shoes and the level track
surface on which she is running. Determine the maxi-
mum acceleration she can achieve. Do you need to
know that her mass is 60.0 kg?

A bullet of mass $0.01\text{kg}$ is fired from a gun weighing $2\text{kg}$. Calculate the velocity with which the gun recoils if $10$ bullets are fired at the same time with a speed of $250\text{m/s}$. Consider $+vex$ axis along the direction of firing.

Which of the following can be a valid distance time graph?

A constant torque acting on a uniform circular wheel changes its angular momentum from $A_0$ to $4A_0$ in $4$ seconds. The magnitude of this torque is

The plate current in a triode can be written as
$i_p=k{(V_g+\frac{V_p}{\mu })}^{\frac{3}{2}}$
Show that the mutual conductance is proportional to the cube root of the plate current.

Check the validity of the equation: PV = mv^{​​​​​2}​​​​- mgh.Symbols have usual meanings

how to solve a problem in friction if force is applied on the block which are one above the other.they are asking to find the frictional force???give me the steps take any example

A particle is projected from the ground at t = 0 so that on its way it just clears two vertical walls of equal height on the ground. If the particle passes just grazing the top of the walls at time $t=t_1$ and $t=t_2$ then calculate the height of the walls.

Figure (32-E6) shows a part of a circuit. If a current of 12mA exists in the 5 k$\Omega$ resistor, find the currents in the other three resistors. What is the potential difference between the points A and B ?

Figure (32-E6)

The angular speed of a wheel of radius 0.50 m moving with the speed of 20 m/s is:

The average power dissipation in pure resistive circuit is:

A force $\overrightarrow{F}=-K(y\hat{i}+x\hat{j})$ (where K is a positive constant) acts on a particle moving in the x - y plane. Starting from the origin, the particle is taken along the positive x-axis to the point (a, 0) and then parallel to the y-axis to the point (a, a). The total work done by the force on the particle is

The standard resistance coil are made of "manganin" because

A circular road of radius $1000\text{m}$ has a banking angle of ${45}^{\circ }$. The maximum safe speed (in $\text{m/s}$) of a car having a mass $2000\text{kg}$ will be (if the coefficient of friction between the tyres and the road is $0.3$) (Take $g=10{\text{m/s}}^2$)

A person riding a car moving at 72 km/h sounds a whistle emitting a wave of frequency 1250 Hz. What frequency will be heard by another person standing on the road (i) in front of the car (ii) behind the car? Speed of sound in air = 340 m/s.

A rod of mass m and length l is lying on a horizontal table. The work done in making it stand vertically on one end will be

An AC source of angular frequency $\omega$ is fed across a resistor R and a capacitor C in series. The current registered is I. If now the frequency of source is changed to $\frac{\omega }{3}$ (but maintaining the same voltage), the current in the circuit is found to be halved. The ratio of reactance to resistance at the original frequency $\omega$ will be.

The ends of a rod of length $l$ and mass $m$ are attached to two identical springs as shown in figure. The rod is free to rotate about its centre ${}^{\prime }{\text{O}}^{\prime }$. The rod is depressed slightly at end $\text{A}$ and released. The time period of the resulting oscillation is

A plate bent at right angles along its centre line, is placed onto a horizontal fixed cylinder of radius R as shown. The minimum co-efficient of friction between the cylinder and the plate so that plate does not slip off the cylinder will be (Assume mass of plate and cylinder to be same)

In the figure shown, a parallel plate capacitor has a dielectric of width d/2 and dielectric constant K = 2. The other dimensions of the dielectric are same as that of the plates. The plates $P_1$ and $P_2$ of the capacitor have area 'A' each. The energy stored in the capacitor is

A small block of mass ‘m’ is rigidly attached at ‘P to a ring of mass ‘3m’ and radius ‘r’. The system is released from rest at $\theta$ = ${90}^0$ and rolls without sliding. The angular acceleration of hoop just after release (about the centre of the ring) is

A body is moved from rest along a straight line by a machine delivering constant power. The velocity of the body as a function of time is proportional to,

A spherical ball of radius $5.5\text{cm}$ is oscillating in a hemispherical bowl. If the time taken to complete one oscillation by the ball is $\frac{\pi }{2}s$, then find the radius of hemispherical bowl.

Two identical capacitors 1 and 2 are connected in series to a battery as shown in figure. Capacitor 2 contains a dielectric slab of constant K. $Q_1$ and$Q_2$ are the charges stored in $C_1$ and $C_2$. Now, the dielectric slab is removed and the corresponding charges are $Q_1^{\prime }$ $Q_2^{\prime }$. Then

The potential energy of a particle of mass m is given by V(x) =$\{\begin{array}{c}{E}_0,0\le x\le 1\\ 0,x>1\end{array}$

${\lambda }_1$ and ${\lambda }_2$ are the de-Broglie wavelengths of the particle, when $0\le x\le 1$ and x > 1respectively. If the total energy of particle is $2E_0$, then $\frac{{\lambda }_1}{{\lambda }_2}$ is

Two balls fastened to light string of same length $l$ and of different masses $m$ & $2m$. The other end of the strings are fixed at $O$. If both the masses collide with same speed (just before collision). Find the ratio of heights raised by the balls.
[Consider, collision is elastic.]

Suppose that the electromagnetic wave in vacuum is
$\overrightarrow{E}=\{\left(3.1\frac{N}{C}\right)\cos \left[(1.8\frac{rad}{m}\right)y+(5.4\times {10}^6\frac{rad}{s})t]\hat{i}$
What is the wavelength $\lambda$?