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Figure depicts the motion of a particle moving along an x axis with a constant acceleration. The figure's vertical scaling is set by $x_s$ = 6.0 m. What is the particle's acceleration?

$S_1$ and $S_2$ are two sources of light which produce individually disturbance at point P given by $E_1=3sin\omega t,E_2=4cos\omega t$. Assuming ${\overrightarrow{E}}_1$ and ${\overrightarrow{E}}_2$ to be along the same line, find the resultant amplitude after their superposition.

The acceleration of a particle performing S.H.M. is 12cm/$se{c}^2$ at a distance of 3 cm from the mean position. Its time period is

An object is displaced from point $A(0,1,2)m$ to a point $B(1,2,3)m$ under the influence of a force $\overrightarrow{F}=2x\hat{i}+3y^2\hat{j}+\hat{k}.$ The workdone by this force is

A source of sound with adjustable frequency produces 2 beats per second with a tuning fork when its frequency is either 476 Hz or 480 Hz. What is the frequency of the tuning fork ?

A cylindrical rod magnet has a length of 5 cm and a diameter of 1 cm. It has a uniform magnetisation of $5.30\times {10}^{3}Amp/m^3$. What its magnetic dipole moment

A boat is moving with a velocity $3\hat{i}+4\hat{j}$ with respect to ground. The water in the river is moving with a velocity $-3\hat{i}-4\hat{j}$ with respect to ground. The relative velocity of the boat with respect to water is

A mass of 100 gm is tied to one end of a string 2 m long. The body is revolving in a horizontal circle making a maximum of 200 revolutions per min. The other end of the string is fixed at the centre of the circle of revolution. The maximum tension that the string can bear is (approximately)

A pipe of length $120cm$ is closed at one end. If the speed of sound in air at given temperature is $360m/s$, locate the nearest pressure antinode from the open end,at frequency $225Hz$.

Each of the batteries shown in figure (35-E8) has an emf equal to 5 V.Show that the magnetic field B at the point P is zero for any set of values of the resistances.

A particle having a charge of $2.0\times {10}^{-4}C$ is placed directly below and at a separation of 10 cm from the bob of a simple pendulum at rest. Teh mass of the bob be given so that the string becomes loose?

Two identical bar magnets with a length 10 cm and weight 50 gm-weight are arranged freely with their like poles facing in a inverted vertical glass tube. The upper magnet hangs in the air above the lower one so that the distance between the nearest pole of the magnet is 3mm. Pole strength of the poles of each magnet will be

An ammeter is to be constructed which can read currents up to 2.0 A. If the coil has a resistance of 25 $\Omega$ and takes 1 mA for full-scale deflection, what should be the resistance of the shunt used ?

A converging lens of focal length 15 cm and a converging mirror of focal length 10 cm are placed 50 cm apart. If a pin of length 2.0 cm is placed 20 cm from the lens farther away from the mirror, where will the final image form and what will be the size of the final image ?

Two balls having masses m and 2m are fastened to two light strings of same length l (figure 9-E18). The other ends of the strings are fixed at O. the strings are kept in the same horizontal line and the system is released from rest. The collision between the balls is elastic. (a) Find the velocities of the balls just after their collision. (b) How high will the balls rise after the collision ?

A square of side 3 cm is placed at a distance of 25 cm from a concave mirror of a focal length of 10 cm. The center of the square is at the axis of the mirror and the plane is normal to the axis. The area enclosed by the image of the square is

A sphere of mass 20 kg is suspended by a metal wire of unstretched length 4m and diameter 1 mm. When in equilbrium, there is a clear gap of 2 mm between the sphere and the floor. The sphere is gently pushed aside so that the wire makes an angle $\theta$ with the vertical and is released. Find the maximum value of $\theta$ so that the sphere does not rub the floor. Young modulus of the metal of the wire is $2.0\times {10}^{11}N{m}^{-2}.$ Make appropriate approximations.

An electric bulb of volume 250 cc was sealed during manufacturing at a pressure of ${10}^{-3}$ mm of mercury at ${27}^0$C. Compute the number of air molecules contained in the bulb. Avogadro constant= 6 $\times$ ${10}^{23}$ $mo{l}^{-1}$, density of mercury = 13600 kg $m^{-3}$and g = 10 m $s^{-2}$.

In P-type semiconductor, there is

The surface of the earth receives solar radiation at the rate of 1400 $W{m}^{-2}$. The distance of the centre of the sun from the surface of the earth is $1.5\times {10}^{11}m$ and the radius of the sun is $7.0\times {10}^{8}m$. Treating the sun as a back body, it follows from the above data that the surface temperature of the sun is about

The pressure of a medium is charged from $1.01\times {10}^5$ Pa to $1.165\times {10}^5$ Pa and change in volume is 10% keeping temperature constant. The bulk modulus of the medium is.

The path of a projectile is given by $y=ax-b{x}^2$. What is the value of the angle ${\theta }_0$ and speed $v_0$ , about a point at which the projectile is launched?

A shell of mass ‘2m’ fired with a speed ‘u’ at angle ${}^{\prime }{\theta }^{\prime }$ to the horizontal explodes at the highest point of its trajectory into two fragments of mass ‘m’ each. If one fragment falls vertically, the distance at which the other fragment falls from the gun is given by

Two sound waves move in the same direction in the same medium. The pressure amplitudes of the waves are equal but the wavelength of the first wave is double the second. Let the average power transmitted across a cross section by the first wave be $P_1$ and that by the second wave be $P_2$. Then

A network of resistances is constructed with $R_1$ and $R_2$ as shown in the figure. The potential at the points 1, 2, 3 … n are $V_1,V_2,V_3,\dots V_n$ respectively, each having a potential k times smaller than the previous one.

The current that passes through the resistance $R_2$ nearest to the $V_{\alpha }$ is

The electric field in an electromagnetic wave is given by $E=\left(50N{C}^{-1}\right)\sin \omega (t-\frac{x}{c})$.
Find the electrical energy contained in a cylinder of cross-section 10 $c{m}^2$ and length 50 $cm$ along the x-axis.

The system is released from rest and the block of mass $1\text{kg}$ is found to have a speed of $0.3\text{m/s}$ after it has descended through a distance of $1\text{m}$. The value of coefficient of kinetic friction is

A projectile is to be launched at an angle ${45}^{\circ }$ so that it falls beyond the pond of length $13.6$ $\text{m}$ as shown in the figure and distance between both the points $O$ to $P$ and $M$ to $N$ is $6$ $\text{m}$. What is the range of values of initial velocity (in $m/s$) so that the projectile falls between points $M$ and $N$.

A particle performs uniform circular motion with an angular momentum $L$. If the frequency of particle's motion is doubled and its kinetic energy halved, the angular momentum becomes

What should be the value of coefficient of static friction between the tyre and the road, when a car travelling at speed of $60km{h}^{-1}$ makes a level turn of radius $40\text{m}$?

A circular hole of diameter 0.15 cm is placed 2.1 m from a screen. On illuminating it by light of wavelength $5\times {10}^{-7}m$ the width of central maxima will be

In an experiment to measure the internal resistance of a cell by a potentiometer, it is found that the balance point is at a length of $2\text{m}$, when the cell is shunted by a $5\Omega$ resistance and at a length of $3\text{m}$, when the cell is shunted by a $10\Omega$ resistance. The internal resistance of the cell is

Find the minimum force 'F' and the angle '$\alpha$' at which it should be applied to a block of mass 'm' kept on a horizontal surface such that the block starts moving. Given that the coefficient of friction between the block and surface is $\mu$.

When we raise our right hand in front of a mirror we see that the image seems to raise its left hand. This phenomenon is known as:

The slope of the graph of the maximum kinetic energy (in joule) of the photoelectrons versus the frequency difference $(v-v_0)$ in a photoelectric experiment is a measure of