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According to Wien's displacement law:

A small stone of mass $200\text{g}$ is tied to one end of a string of length $80\text{cm}$. Holding the other end in the hand, the stone is whirled in a vertical circle. What is the minimum speed that needs to be imparted at the lowest point such that the stone is just able to complete the vertical circle?(Take $g=10\text{m}/s^2$)

In a system of units if force $\left(F\right)$, acceleration $\left(A\right)$ and time $\left(T\right)$ are taken as fundamental units, then the dimensional formula of energy is:

Two forces, whose magnitude are at the ratio of 3:5 give a resultant of 35 N. If angle of inclination is 60^o, then the magnitude of each force is:

The displacement equation of a particle is $x=3\sin 2t+4\cos 2t$. The amplitude and maximum velocity will be respectively

In a resonance column experiment, a tuning fork of frequency 400 Hz is used. The first resonance is observed when the air column has a length of 20.0 cm and the second resonance is observed when the air column has a length of 62.0 cm. (a) Find the speed of sound in air. (b) How much distance above the open end does the , pressure node form ?

What is mean by torque

The gap between the plates of a plane capacitor is filled with an isotropic insulator whose dielectric constant varies in the direction perpendicular to the plates according to the law $K=K_1[1+\sin \frac{\pi }{d}x]$, where $d$ is the separation between the plates and $K_1$ is a constant. The area of the plates is $S$. Then the capacitance of the capacitor is

A point charge $+10\text{nC}$ is located on the axis of a disc of radius $1\text{m}$ at a distance of $\sqrt{3}\text{m}$ from the plane of the disc as shown in the figure. The electric flux from the charge passing through the disc is

(Take ${ϵ}_o=9\times {10}^{-12}{\text{C}}^2/{\text{N-m}}^2$)

A conducting circular loop is placed in a uniform magnetic field $0.04T$ with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at a rate of $2mm/s$. Find the induced emf in the loop when the radius of the loop is $2cm$.

Evaluate: $\int \left(\cos \right(x)+x^2)dx$

Each of the three plates shown in the figure has area of $400{\text{cm}}^2$ on one side and the gap between the adjacent plates is $8.85\text{mm}$. The equivalent capacitance of the system is

A toy car with charge $q$ moves on a frictionless horizontal plane surface under the influence of a uniform electric field $\overrightarrow{E}$. Due to the force $q$$\overrightarrow{E}$, its velocity increases from $0m/s$ to $6m/s$ in one second. At that instant the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between $0$ to $3$ seconds are respectively

Figure shows four situations in which a force acts on a box while the box slides rightward a distance d across a frictionless floor. The magnitude of the forces are identical with their orientations as shown. Identify under which condition the work done on the box during the displacement will be negative.

Which of the following do not depend on frame of reference?
1. Mass
2. Distance between two points
3. Velocity
4. Distance

A tungsten. The cathode and a thoriated - tungsten cathode have the geometrical dimensions and are operated at the same temperature. The thoriated tungsten cathode gives 5000 times more current than the other one. Find the operating temperature. Take relevant data from the previous problem.

Consider a rain drop of mass $1\text{g}$ falling from a height of $2\text{km}$. It hits the ground with a speed of $50\text{m/s}$. The work done by resistive force of air is
$(g=10{\text{m/s}}^2)$

If the surface area of a cube is increasing at a rate of $3.6{\text{cm}}^2/\text{sec}$ retaining its shape, then the rate of change of its volume (in ${\text{cm}}^3/\text{sec}$) when the length of a side of the cube is $10\text{cm}$ is:

the energy per quantum associated with the light of wavelength 5890$A^o$

A rod $CD$ of thermal resistance $5.0{\text{KW}}^{-1}$ is joined at the middle of an identical rod $AB$ as shown in the figure. The ends $A,B$ and $D$ are maintained at ${100}^{\circ }\text{C}$, $0^{\circ }\text{C}$ and ${25}^{\circ }\text{C}$ respectively. Find the heat current in $CD$.

System is released from rest. Find speed of the blocks after 2 seconds.

Find the time period of meeting of the minute hand and second hand of a clock. (Initial positions are shown in the figure below)

In an experiment, electrons are accelerated, from rest, by applying a voltage of $500\text{V}$. Calculate the radius of the circular path if a magnetic field $100\text{mT}$ is then applied.

$[\text{Charge of the electron,}e=1.6\times {10}^{-19}\text{C}\text{Mass of the electron,}{m}_e=9.1\times {10}^{-31}\text{kg}]$

The roughness coefficient for the channel is given as f. The Chezy's coefficient is directly proportional to_____.

A long straight wire in
the horizontal plane carries a current of 50 A in north to south
direction. Give the magnitude and direction of B at a point
2.5 m east of the wire.

What is the relationship between the angle of incidence and the angle of reflection?