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A hollow conducting sphere of radius $R$ and total charge $q$ rotates about its diametrical axis with constant angular speed $\omega$. The magnitude of magnetic moment of the sphere is :

The driver of a car travelling with speed $30\text{m/s}$ towards a cliff , sounds a horn of frequency $600\text{Hz}$. If the velocity of sound in air is $330\text{m/s}$, the frequency of sound heard by the driver reflected off the cliff is



[Assume, medium is stationary]

When a current $I$ is set up in a wire of radius $r$, the drift velocity is $v_d$. If the same current is set up through a wire of radius $2r$ of the same material, the drift velocity will be

A player stops a football weighing $0.5\text{kg}$ which comes flying towards him with a velocity of $10\text{m/s}$. If the impact lasts for $1/50\text{th}$ sec. and the ball bounces back with a velocity of $15\text{m/s}$, then the average force involved is

Draw V-I characteristics of a p-n junction diode. Answer the following questions, giving reasons :
(i) Why is the current under reverse bias almost independent of the applied potential upto a critical voltage?
(ii) Why does the reverse current show a sudden increase at the critical voltage?
Name any semiconductor device which operates under the reverse bias in the breakdown region.

Unit vector of $\overrightarrow{A}$ is equal to

What is electrochemical equivalence and equivalent weight?

In the figure shown, the tension at the midpoint of the rope of mass $3\text{kg}$ (point $B$) is $13\text{N}$. Find the force pulling the $5\text{kg}$ body.

To decrease the range of an ammeter its resistance need to be increased. An ammeter has resistance $R_0$ and range I. Which of the following resistance can be connected in series with it to decrease its range to $\frac{I}{n}$?

A boat crosses a river from port $A$ to port $B$, which are directly opposite to each other. The speed of the water is $v_w$ and that of boat is $V_b$ relative to water. Assume $V_b=2V_w$. The time taken by the boat, if it has to cross the river directly on the $AB$ line is $(\text{given}AB=D)$

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).

A
compass needle free to turn in a horizontal plane is placed at the
centre of circular coil of 30 turns and
radius 12 cm. The coil is in a vertical plane making an angle of 45º
with the magnetic meridian. When the current in the coil is 0.35 A,
the needle points west to east.

(a) Determine the
horizontal component of the earth’s magnetic field at the
location.

(b) The current
in the coil is reversed, and the coil is rotated about its vertical
axis by an angle of 90º in the anticlockwise sense looking from
above. Predict the direction of the needle. Take the magnetic
declination at the places to be zero.

In the following circuit all are 4 $\times$ 1 multiplexer. The output f is

Two forces $P$ and $Q$ act such that the resultant $R$ is equal to the magnitude of $P$. If $P$ is doubled, what is the angle made by the new resultant with the force $Q$?

A projectile of mass $0.5kg$ is thrown with a velocity of $30m/s$ at an angle of ${60}^0$ with the horizontal. Find its momentum at highest point.

A vertical frictionless semicircular track of radius $1\text{m}$ is fixed on the edge of a movable trolley (figure). Initially the system is at rest and a mass $m$ is kept at the the top of the track. The trolley starts moving to the right with a uniform horizontal acceleration $a=\frac{2g}{9}$. The mass slides down the track, eventually losing contact with it and dropping on to the floor. Calculate the angle $\theta$ at which it loses contact with the trolley and the track.

Electric field in a region is $E=5\times {10}^{5}N{C}^{-1}$ making an angle of ${37}^{\circ }$ with x-axis. The magnitude of the potential difference between origin and point cm is

Find the rotation at B for the frame shown below.

A body starts from rest and travels with uniform acceleration such that it covers $8m$ during the $2^{nd}$ second. The distance it would travel during the $5^{th}$ second is

Question 6

The sound from a mosquito is produced when it vibrates its wings at an average rate of 500 vibrations per second. What is the time period of the vibration?

The velocity–displacement graph of a particle is shown in the figure.

The acceleration–displacement graph of the same particle is represented by :

Blocks A and B in the fig. Are connected by a bar of negligible weight. Mass of each block is 170 kg and ${\mu }_A$ = 0.2 and ${\mu }_B$ = 0.4, where ${\mu }_A$ and ${\mu }_B$ are the coefficients of limiting friction between blocks and plane, calculate the force developed in the bar (g=10 $m{s}^{-2}$)

A ball P is dropped vertically and another ball Q is thrown horizontally with the some velocity from the same height and at the same time. If air resistance is neglected, then

A steel wire of original length 1 m and cross-sectional area $4.00m{m}^2$ is clamped at the two ends so that it lies horizontally and without tension. If a load of 2.16 kg is suspended from the middle point of the wire, what would be its vertical depression ?

Y of the steel = $2.0\times {10}^{11}N{m}^{-2}.Takeg=10m{s}^{-2}$.

Four charges $q_1=1\mu \text{C}$, $q_2=2\mu \text{C}$, $q_3=-3\mu \text{C}$ and $q_4=4\mu \text{C}$ are kept on the vertices of a square of side $1\text{m}$. Find the electric potential energy stored in this system of charges.