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A horizontal rod $0.2\text{m}$ long is mounted on a balance and carries a current. At the location of the rod, a uniform horizontal magnetic field has a magnitude $0.067\text{T}$ and direction perpendicular to the rod. The magnetic force on the rod is measured by a balance and found to be $0.13\text{N}$. What is the current ?

A parallel plate capacitor is charged to a certain potential difference. A dielectric slab of thickness $4.8\text{mm}$ is inserted between the plates and it becomes necessary to increase the distance beteeen the plates by $4\text{mm}$ to maintain the same potential difference. The dielectric constant of the slab is :

Figure shows two adiabatic vessels each having $m\text{gm}$ of water at different temperatures. The ends of a metal rod of length $L$, area of cross section $A$, and thermal conductivity $K=\frac{msL}{2A}$ [where $s$ is the specific heat capacity of water] are connected to the water in the vessels as shown in the figure. Find the time taken for the difference in temperature of the vessels to become half of the original value.

According to right hand thumb rule, in a cyclotron when magnetic field is coming out the particle should move anticlockwise but it does move clockwise, why is that so?

Particles of masses 1 g, 2 g, 3 g,........100 g are kept at the marks 1 cm, 2 cm, 3 cm, ........100 cm respectively on a metre scale. What is the moment of inertia of the system of particles about a perpendicular bisector of the metre scale?

Find the electric field at point $\text{P}$ as shown in figure due to an infinite long uniformly charged non-conducting thick sheet.

A charge $Q$ is placed symetrically at the centre of a closed cylinder as shown in the figure. If $\alpha ={60}^{\circ }$ then the flux associated with the curved surface of the cylinder will be

In the circuit shown in the figure, the $\text{AC}$ source gives a voltage $V=20\cos 2000t$. If the reading of voltmeter is $V_1$, ammeter is $A_1$ and the power consumed by the circuit is $P$, then:

A rod of length $10\text{m}$ is inclined on the wall at an angle ${37}^{\circ }$ with horizontal.





Find out position of centre of mass of the rod assuming the wall to be along $y-$ axis and foot of the wall as the origin.

An electric dipole of dipole moment $P$ is placed parallel to a uniform electric field of magnitude $E.$ The amount of work done in slowly rotating the dipole by ${60}^{\circ }$ will be



$[$0.77 Mark$]$

In Young's double slit experiment, the two slits are illuminated by light of wavelength $5890\stackrel{\circ }{A}$ and the angular fringe width is ${0.2}^{\circ }$. If the whole apparatus is immersed in water, then the new angular fringe width will be (refractive index of water $=\frac{4}{3}$).

Which of the following physical quantity is dimensionless?

The potential energy for a force field $\overrightarrow{F}$ is given by $U(x,y)=\sin (x+y)$. The force acting on the particle of mass $m$ at $(0,\frac{\pi }{4})$ is (in $N$)

Three rods of same material, same area of cross-section but different lengths $10\text{cm}$, $20\text{cm}$ and $30\text{cm}$ are connected at a point as shown in the figure. Find the temperature of junction ${}^{\prime }{\text{O}}^{\prime }$.

According to Bohr's theory the radius of electron in an orbit described by principal quantum number n and atomic number Z is proportional to

Initially three bodies of mass $2m,2m$ and $3m$ are placed on the $x$-axis at position $x=1,x=2$ and $x=4$. If a body of mass $4m$ is placed at origin, then find the displacement of centre of mass from initial position.

$E_{0}and{E}_h$ respectively represent the average kinetic energy of a molecule of oxygen and hydrogen. If the two gases are at the same temperature, which of the following statements is true?

The frequency of $K_{\alpha }$ line of a source of atomic number Z is proportional to

The magnetic field varies with time as $B=0.5t^2$, in a square coil of side $10\text{cm}$, kept with its plane perpendicular to the field. If the resistance of the coil is $5\times {10}^{-2}\Omega ,$ the total charge that flows through it from $t=0$ to $t=2\text{sec}$ will be:

A rod of length $10\text{cm}$ made up of conducting and non-conducting material (shaded part is non-conducting). The rod is rotated with constant angular velocity $10\text{rad/s}$ about point $O$, in constant magnetic field of $2\text{T}$ as shown in the figure. The induced emf between the point $\text{A}$ & $\text{B}$ of the rod will be:

A continuous time signal x(t) is defined as

$x\left(t\right)=2+\cos \left(50\pi t\right)$ is sampled with sampling interval $T_s=0.025sec$ and passed through an ideal low pass filter whose frequency response is as shown in figure below



The spectrum of output will be

Particle $\text{A}$ moves with speed $10\text{m/s}$ in a frictionless circular fixed horizontal pipe of radius $5\text{m}$ and strikes with $\text{B}$ of double mass that of $\text{A}$. Coefficient of restitution is $\frac{1}{2}$ and particle $\text{A}$ starts its journey at $t=0$. The time at which the second collision occurs is

A transparent thin plate of a polaroid is placed on another similar plate such that, the angle between their transmission axes is ${30}^{\circ }$. The intensities of the emergent and, the unpolarized incident light, will be in the ratio,

A wheel starting from rest is uniformly accelerated at $2{\text{rad/s}}^2$ for 20 seconds. It rotates uniformly for the next 20 seconds and is finally brought to rest in the next 20 seconds. Total angular displacement of the wheel in radians is

A non-conducting disc of radius $R$, having uniformly distributed positive charge $Q$ on the surface, is rotating about its axis with uniform angular velocity $\omega$. The magnetic moment of the disc is-

The potential energy of a particle executing simple harmonic motion at a distance x from the equilibrium position is proportional to