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Two rods $A$ and $B$ of different materials but same cross section are joined as shown in figure. The free end of $A$ is maintained at ${100}^{\circ }C$ and the free end of $B$ is maintained at $0^{\circ }C$. If $l_2=2l_1,K_1=2K_2$ and rods are thermally insulated from sides to prevent heat losses, then the temperature $\theta$ of the junction of the two rods is

A prismatic, straight, elastic, cantilever beam is subjected to a linearly distributed transverse load as shown below. If the beam length is L,Young's modulus E and area moment of inertia I, the magnitude of the maximum deflection is

A simple pendulum of mass m and charge q is hanging from the roof of a car moving on a circular track of. Radius r with a speed v . At equillibrium pendulum string makes angle a with equillibrium . Find magnitude and direction of E required so that the string makes same angle a on other side of vertical

A parallel plate capacitor with air as medium between the plates has a capacitance of 10μF. The area of capacitor is divided into two equal halves

and filled with two media as shown in the figure having dielectric constant k₁=2 and k₂=₄. The capacitance of the system will now be

If a light ray from air enters three different media in such a way that the refracted angles are ${45}^0$, ${30}^0$ and ${60}^0$ respectively. Identify the right statement with respect to the optical density of these media.

The unit for molar susceptibility is

A proton and an $\alpha -$particle enters a uniform magnetic field in a perpendicular direction with the same speed. If the proton takes $25\mu \text{s}$ to make $5\text{revolutions}$, then the time period for the $\alpha -$particle will be:

A cycle can bend upto a maximum angle of ${45}^{\circ }$. If the radius of the bend is $10\text{m}$, then what should be the maximum speed of the cyclist so that he does not crash?

What is the ratio of the angular velocity of the hour hand of a watch to the angular velocity of Earth's rotation about its axis?

When a body is projected with velocity $\overrightarrow{v},$ horizontally from a height $h$.



$\begin{array}{cc}\text{Column-I}& \text{Column-II}\\ \text{(a) The speed of body at any time}t\text{is}& \text{(p)}\sqrt{\frac{2gh}{u^2}}\\ \text{(b) It will strike the ground after time}t\text{is equal to}& \text{(q)}\sqrt{\frac{2h}{g}}\\ \text{(c) The path followed by the body is expressed as}y\text{equal to}& \text{(r)}\frac{1}{2}g\frac{x^2}{u^2}\\ \text{(d) The value of}\tan \theta \text{, where}\theta \text{is the angle made by velocity striking the ground with horizontal is equal to}& \text{(s)}\sqrt{v^2+g^2{t}^2}\end{array}$

A $5ampere$ current is passed through a solution of zinc sulphate for $40minutes$. The amount of zinc deposited at the cathode is:

In absorbtion spectra,we pass em radiation thorugh unexited atoms .

(a)they absorb some energy, of which corresponding black bands are seen on the photoelectric plate. If they absorb energy from the light, that means the atoms went to an excited state((do all of them absob energy from light?)). so when they would return back to the ground state, they should emit radiation of the same wavelength, if they do why do we see black bands then?(i m talking abt absorbtion spectra)

An $AC$ voltage $E=220\sin (\omega t-\frac{\pi }{6})$ is connected across a certain device. The current flowing through this device is $i=115\sin (\omega t+\frac{\pi }{3})$. The correct phasor diagram, of applied voltage and current flowing in the circuit, is,

An $U-$ tube of base length ${}^{\prime }{l}^{\prime }$ filled with the same volume of two liquids of densities $\rho$ and $2\rho$ is moving with an acceleration ${}^{\prime }{a}^{\prime }$ on the horizontal plane, as shown in the figure. If the difference in heights of the liquid columns in the two vertical limbs (open to the atmosphere) is zero, then the height $h$ is given by

A spring having with a spring constant 1200 N m^–1
is mounted on a horizontal table as shown in Fig. A mass of 3 kg is
attached to the free end of the spring. The mass is then pulled
sideways to a distance of 2.0 cm and released.

Determine (i) the frequency of oscillations, (ii) maximum
acceleration of the mass, and (iii) the maximum speed of the mass.

A spherical conductor of radius $R$ carries charge $Q$ on its surface. The value of electric field just outside the surface of the conductor is $E$. If the radius of the counductor is doubled while keeping the charge same, what will be the value of new electric field just outside the surface of the conductor?

A rigid massless beam is balanced by a body of mass $4m$ on the left hand side and a pulley-mass system on the right hand side. The value of $\frac{x}{y}$ is :
(Consider the rope and pulley to be massless).

The velocity of a particle is V=V0+gt+ft if its position is X=0 at t=0 then it's displacement after unit time t=1 is

A) V0 +(g/2) +(f/3)

B) V0 +g +f

C) V0 + (g/2) + f

D) V0 + 2g + 3f

The radius of gyration of a uniform disc about a line perpendicular to the disc equals its radius. Find the distance of the line from the centre.

A wire of density $\rho$ is stretched between two clamps a distance $L$ apart, while being subjected to an extension $l$. Y is the Young's modulus of the material of the wire. The lowest frequency of transverse vibrations of the wire is given by

A capillary tube of radius $r$ is immersed in water and water rises in it to a height $h$. The mass of water in the capillary tube is $5\text{g}$. Another capillary tube of radius $2r$ is immersed in water. The mass of water that will rise in this tube is:

The susceptibility of magnesium at 300 K is 1.2 $\times {10}^{-5}$. At what temperature will the susceptibility increase to 1.8 $\times {10}^{-5}$ ?

In the figure, a rod closing the circuit moves along a $U-$shaped wire at a constant speed $v$ under the action of the force $F$. The circuit is in a uniform magnetic field perpendicular to its plane. Calculate $F$, if the rate of generation of heat is $P$.

In the given figure, a particle of mass $1\text{kg}$ is projected at $t=0$. The angle made by the particle with the horizontal after $2\text{seconds}$ is

A coil carries a current and experiences a torque due to a magnetic filed. The value of the torque is 80% of the maximum possible torque. The angle between the magnetic field and the normal to the plane of the coil is

A ring of mass $0.250\text{kg}$ and radius $200\text{cm}$ and another ring of mass $0.500\text{kg}$ and radius $400\text{cm}$ have the same center. Find the moment of inertia of the system of two rings about the axis passing through their centers and perpendicular to their plane.

The
velocity associated with a proton moving in a potential difference of
1000 V is 4.37 × 10⁵
ms^–1.
If the hockey ball of mass 0.1 kg is moving with this velocity,
calculate the wavelength associated with this velocity.

Maximum sound pressure tolerable by the human ear is $30{\text{N/m}}^2$. For sound of frequency ${10}^3\text{Hz}$ and speed $300\text{m/s}$, the maximum displacement of particles of medium is
[density of air $1.5{\text{kg/m}}^3)$]

A spring has a certain mass suspended from it and its period for vertical oscillation is T. The spring is now cut into two equal halves and the same mass is suspended from one of the halves. The period of vertical oscillation is now