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An uniform rod of mass $3\text{kg}$ is hinged at the wall and connected through a light string as shown in the figure. Find the tension in the string.(Take $g=10{\text{m/s}}^2$).

In the given circuit, the potential difference across the capacitor is $10\text{V}$. Each resistance is $3\Omega$. The cell is ideal. The emf of the cell is

A uniform electric field pointing in positive $\text{x-}$direction exists in a region. Let $\text{A}$ be the origin, $\text{B}$ be the point on the $\text{x-}$axis at $x=+1\text{cm}$ and $\text{C}$ be the point on the $\text{y-}$ axis at $y=+1\text{cm}$. Then, the potentials at the points $\text{A, B}$ and $\text{C}$ satisfy

What is the intensity of gravitational field of the centre of a uniform spherical shell

The displacement $Y$ of a particle executing simple harmonic motion is given by



$Y=2\sin t{\cos }^2\frac{t}{2}$



This expression may be considered to be a result of the superposition of how many simple harmonic motions?

A rod $AB$ of length $L$ is hung from two identical wires $1$ and $2$. A block of mass $m$ is hung at point $O$ of the rod as shown in Fig. The value of $x$ so that a tuning fork excites the fundamental mode in wire $1$ and the second harmonic in wire $2$ is

The potential energy of a body is given by $A-B{x}^2$ (where x is the displacement). The magnitude of force acting on the particle is

Three identical circular planner disc each of mass $m$ and radius $r$ are welded as shown in figure. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point $P$ is

In the experiment on photoelectric effect, the graph between $E_{max}$ and $v$ is found to be straight line as shown in figure.



The threshold frequency and Planck's constant according to this graph are

The current through a wire depends on time as $i=(2+3t)\text{A}$. Calculate the charge that crossed through the cross-section of the wire in first $10\text{seconds}$.

An iron rod of susceptibility $599$ is subjected to a magnetising field of $1200{\text{Am}}^{-1}$. The permeability of the material of the rod is :$({\mu }_0=4\pi \times {10}^{-7}{\text{T mA}}^{-1})$

Water and turpentine oil (specific heat less than that of water) are both heated to same temperature. Equal amounts of these placed in identical calorimeters are then left in air

A gas has molar heat capacity $C=37.35\text{J}{\text{mol}}^{-1}{\text{K}}^{-1}$ in the process $PT=\text{constant}$. Find the number of degrees of freedom of molecules in the gas.

The energy of a photon of light with wavelength $5000\stackrel{\circ }{A}$ is approximately 2.5 eV. This way the energy of an X-ray photon with wavelength $1\stackrel{\circ }{A}$ would be

A flat plate is moving normal to its plane through a gas under the action of a constant force $F$. The gas is kept at a very low pressure. The speed of the plate $v$ is much less than the average speed $u$ of the gas molecules. Which of the following options is/are true?

A long straight wire of radius $a$ carries a steady current $I$. The current is uniformly distributed across its cross-section. The ratio of the magnetic field at distance $\frac{a}{2}$ and $2a$ from axis of wire is

A combination of logic gates has the truth table below.

At a hydroelectric power plant, the water pressure head is at a height of $300\text{m}$ and the water flow available is $100{\text{m}}^3{\text{s}}^{-1}$. If the efficiency of the AC generator, coupled with the turbine, is $60\%$, estimate the electric power available from the plant.



Take, $g=9.8{\text{ms}}^{-2}$

If $f\left(x\right)=x\cos x$, find $f^{\prime \prime }\left(x\right)$.

A uniform rod of mass $2\text{kg}$ and length

$3\text{m}$ is bent in the form of an equilateral triangle. The moment of inertia of the triangle about a vertical axis perpendicular to the plane of the triangle and passing through the center is

A block $m_1$ of mass $2.0\text{kg}$ is moving on a frictionless horizontal surface with a velocity of $1.0\text{m/s}$ towards another block $m_2$ of equal mass kept at rest as shown. The spring constant of the spring fixed at one end of $m_2$ is $100\text{N/m}$. The maximum compression of the spring is

An insect of negligible mass is sitting on a block of mass $M$, tied with a spring of force constant $k$. The block performs simple harmonic motion with amplitude $A$ in front of a plane mirror as shown. The maximum speed of the insect relative to its image will be

Find mutual induuctance of the two co-planar coils as shwon $(r<<a;r<<b)$



Diagram

A string of length $7\text{m}$ has a mass of $0.035\text{kg}$. If the tension in the string is $60.5\text{N}$, then speed of a wave on the string is: