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A conductor of length $0.04\text{m}$ is tangentially connected to a circular loop of radius $0.03\text{m}$ perpendicular to its plane. Find the magnetic field induction at the centre of the loop, if $4\text{A}$ current is passed through the conductor as shown in figure.

Two waves represented by $y_1=3\sin (2000\pi t-50x)$ and
$y_2=3\sin (2008\pi t+50x)$ are approaching each other. The number of beats heard per second will be
(Assume SI units)

The weight of an object at the center of a planet of radius R is:

An arrangement of three infinitely long straight wires placed perpendicular to plane of paper carrying same current $I$ along the same direction is shown in the figure. The magnitude of force per unit length on wire $\text{B}$ is

A particle executes simple harmonic motion between x = -A and x=+ A. The time taken for it to go from the mean position, O to $\frac{A}{2}$ is $T_1$ and to go from $\frac{A}{2}$ to A is $T_2$. Then,

As shown in figure, the block B of mass m starts from the rest at the top of a wedge W of mass M. All surfaces are without friction. W can slide on the ground, B slides down onto the ground, moves along it with a speed v, has an elastic collision with wall, and climbs back onto W. Then:

A beam of plane polarised light of large cross-sectional area and uniform intensity of $3.3{\text{Wm}}^{-2}$ falls normally on a polariser (cross-sectional area $=3\times {10}^{-4}{\text{m}}^2$) which rotates about its axis with an angular speed of $31.4{\text{rad s}}^{-1}.$ The energy of light passing through the polariser per revolution, is close to-

Three uncharged capacitors of capacitance $1\mu \text{F}$, $2\mu \text{F}$ and $3\mu \text{F}$ are connected as shown in figure. If potentials at $\text{P,Q}$ and $\text{R}$ are $1\text{V},2\text{V}$ and $3\text{V}$ respectively. Then potential at $\text{O}$ is

A fan is rotating with angular velocity 100 revs/sec. Then it is switched off. It takes 5 minutes to stop.
(i) Find the total number of revolutions made before it stops. (Assume uniform angular retardation)
(ii) Find the value of angular retardation.
(iii) Find the average angular velocity during this interval.

In the figure shown about what position does the block perform SHM?[K=10N/m, F= 100N]

For the given equation representing position, $y=\text{A sin}\omega t+A\sin (\omega t+\frac{2\pi }{3})$, match the column.

$\begin{array}{cc}\text{Column I}& \text{Column II}\\ \text{(A) Motion}& \text{(p) Is periodic but not SHM}\\ \text{(B) Amplitude}& \text{(q) Is SHM}\\ \text{(C) Initial phase}& \text{(r) A}\\ \text{(D) Maximum velocity}& \text{(s)}\frac{\pi }{3}\\ & \text{(t)}\frac{\omega }{3}\\ & \text{(u) None}\end{array}$

A block of mass $1\text{kg}$ containing a net positive charge ${10}^{-10}\text{C}$ is placed on a smooth horizontal table which terminates in a vertical wall as shown in figure. The distance of the block from the wall is $2\text{m}$. A horizontal electric field ${10}^{10}\text{N/C}$ towards right is switched on. Assuming elastic collision (if any), find the time period of the resulting oscillatory motion.

For the circuit shown in figure, the capacitance measured between terminals B and Y will be

A beam of light of wavelength $400nm$ from a distant source falls on a single slit $1mm$ wide and the resulting diffraction pattern is observed on a screen $1m$ away. What is the distance between the first dark fringes on either side of central bright fringe?

A sphere of radius $R$ made up of material of relative density $\sigma$ has a concentric spherical cavity of radius $r$. It just floats when placed in a tank full of water. The value of the ratio $\frac{R}{r}$ will be

A person looks at different trees in on open space with the following details. Arrange the trees in decreasing order of their apparent sizes.

$\begin{array}{ccc}& & \\ \underset{–}{\text{Tree}}& \underset{–}{\text{Height (m)}}& \underset{–}{\text{Distance from the eye (m)}}\\ \text{A}& 2.0& 50\\ \text{B}& 2.5& 80\\ \text{C}& 1.8& 70\\ \text{D}& 2.8& 100\end{array}$

Two vessels of different materials are similar in size in every respect. The same quantity of ice filled in them gets melted in 20 minutes and 30 minutes. The ratio of their thermal conductivities will be

A small block is shot into each of the four tracks as shown below. Each of the tracks rises to the same height. The speed with which the block enters the track is the same in all cases. At the highest point of the track, the normal reaction is maximum in

Two particles of masses $m_1,m_2$ moving with initial velocities $u_{1}and{u}_2$. On collision, one of the particles get excited to higher level, after absorbing energy ε . If final velocities of particles be $v_{1}and{v}_2$ then we must have :

In a rocket of mass 1000 kg fuel is consumed at a rate of 40 kg/s. The velocity of the gases ejected from the rocket is $5\times {10}^4$ m/s. The thrust on the rocket is

An electron (of mass $m$) and a photon have the same energy $E$ in the range of a few $\text{eV}$. The ratio of the de-Broglie wavelength associated with the electron and the wavelength of the photon is ($c=$ speed of light in vacuum)

At what temperature root mean square velocity of hydrogen becomes double of its value at $\text{S.T.P}$, keeping pressure constant?

A man weighing 80 kg is standing in a trolley weighing 320 kg. The trolley is resting on frictionless horizontal rails. If the man starts walking on the trolley with a speed of 1 m / s, then after 4 sec his displacement relative to the ground will be

A particle is executing SHM according to the equation, $x=A\cos \omega t$. Average speed of the particle during the interval $0\le t\le \frac{\pi }{6\omega }$ is