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A wire having a linear mass density $5\times {10}^{-3}\text{kg/m}$ is stretched between two rigid supports with a tension of $450\text{N}$. The wire resonates at a frequency of $420\text{Hz}$. The next higher frequency at which the same wire resonates is $490\text{Hz}$. The length of the wire will be

In a series LR growth circuit, the maximum current and maximum induced emf in an inductor of 6 mH are 3A and 8V respectively. In how much time the current in the circuit grows to 63.2% of its final value?

A cylindrical piston of mass $M$ slides smoothly inside a long cylinder closed at one end, enclosing a certain mass of gas.
The cylinder is kept with its axis horizontal. If the piston is disturbed from its equilibrium position, it oscillates simple harmonically. The period of oscillation will be

The latent heat of vaporization of water is $2240\text{J/g}$. If the work done in the process of expansion of $1\text{g}$ is $168\text{J}$, then increase in internal energy is

The speed of sound in hydrogen gas at $\text{STP}$ is $v_o$. The speed of sound in a mixture containing $3$ parts of hydrogen gas and $2$ parts of oxygen gas at $\text{STP}$ will be

Curves of two waves propagating in the same medium is shown. Here, $y$ is displacement in $\text{m}$ and $t$ is time in $\text{s}$. Find the ratio of their average intensities?

What are the dimensions of K (coulomb’s law constant)?

A monochromatic source of light operating at 200 W emits $4\times {10}^{20}$ photons per second. The wavelength of this light will be __ nm.

Find the value of poission's ratio $\left(\mu \right)$ of a material whose bulk modulus$\left(K\right)$ value is half of its young's modulus $\left(Y\right)$ value.

A particle executes linear $\text{SHM}$ of amplitude $A$ along $x-$ axis. At $t=0$ the position of the particle is $x=\frac{A}{2}$ and it moves along $+x$ direction. Find the phase constant $\left(\delta \right)$ if the equation is written as $x=\text{A sin}(\omega t+\delta )$

An open organ pipe has fundamental frequency of $300\text{Hz}$. The first overtone of this organ pipe is same as the first overtone of a closed organ pipe. Find the length of the closed organ pipe?
[speed of sound in air $=330\text{m/s}$]

A couple consisting of two forces $F_1$ and $F_2$ each equal to $5\text{N}$ is acting at the rim of a disc of mass $2\text{kg}$ and radius $0.5\text{m}$ for $5\text{s}$. Initially, the disc is at rest, the final angular momentum of the disc is

Two glass bulbs A and B are connected by a very small tube of negligible volume having a stop cock. Volume of bulb A is 100 cm³ and it contains some gas. Bulb B is empty on opening the stop cock, the pressure dropped by 60%. The volume of Bulb B must be____.

The pressure $P$ of an ideal diatomic gas varies with its absolute temperature $T$ as shown in the figure. The molar heat capacity of the gas during this process is:
[$R$ is the gas constant]

A point mass m is situated inside a thick spherical shell of mass M, inner radius R and outer radius 2R. Work required to take this mass m from inside the shell to infinity, slowly is

The breaking stress of the metal used for the wire connecting the blocks is $2\times {10}^9{\text{N/m}}^2$. Minimum radius of the wire is:
[Take $\sqrt{\frac{400}{6\pi }}=4.60,g=10{\text{m/s}}^2$ for calculation.]

A 6-kg weight is fastened to the end of a steel wire of unstreched length 60 cm. It is whirled in a vertical circle and has an angular velocity of 2 revolution per second at the bottom of the circle. The area of cross-section of the wire is $0.05c{m}^2$. The elongation of the wire when the weight is at the lowest point of the path is $(Y_{steel}=2\times {10}^{11}Pa)$

In Joly's defferential steam calorimeter, 3 g of an ideal gas is contained in a rigid closed sphere at ${20}^{\circ }C.$ The sphere is heated by steam at ${100}^{\circ }C$ and it is found that an extra 0.095 g of steam has condensed into water as the temperature of the gas becomes constant. Calucate the specific heat capacity of the gas in J $g^{-1}$ $K^{-1}$. The latent heat of vaporization of water = 540 cal $g^{-1}$

A glass rod of radius 1mm is inserted symmetrically into a glass capillary tube with inside radius 2mm Then the whole arrangement is brought in contact with the surface of water.Surface tension of water is $7\times {10}^{-2}N/m$.To what height will water rise in the capillary $(\theta =0^o)$

A wire ABCDEF (with each side of length L) bent as shown in Fig. and carrying a current I is placed in a uniform magnetic field B parallel to the positive y - direction. What is the magnitude and direction of the force experienced by the wire?

Two planets move around the sun. The periodic times and the mean radii of the orbits are $T_1,T_{2}and{r}_{1,}{r}_2$ respectively. The ratio $\frac{T_1}{T_2}$ is equal to.

Lift A is going up with velocity 20 m/s and acceleration as $8m/s^2$ in the downward direction. While lift B is going down with 10 m/s and acceleration of $+2m/s^2$ in upward direction. At this moment a bolt in the ceiling of lift A gets loose and falls. Height of the lift is 16 m.

What is the velocity of bolt relative to lift B when it hits the floor of A.?

What is corona discharge?

The vector sum of the forces of 10 Newton and 6 Newton can be

A copper ball contains 4x10²³ atoms. What fraction of the electrons be removed to give the ball a charge of 9.6 micro coloumbs?

Find the time period of meeting of minute hand and second hand of a clock.

Water enters through end A with speed $v_1$ and leaves through end B with speed $v_2$ of a cylindrical tube AB. The tube is always completely filled with water. In case I tube is horizontal and in case II it is vertical with end A upwards and in case III it is vertical with end B upwards. We have $v_1$ = $v_2$ for

Find the total energy of the inclined rod of mass $m$, rotating with an angular velocity $\omega$ about a vertical axis $Y{Y}^{\prime }$ as shown in figure.

A scooter going due east at $10m{s}^{-1}$ turns right through an angle of 90°. If the speed of the scooter remains unchanged in taking turn, the change is the velocity of the scooter is

In a situation, the contact force by a rough horizontal surface on a body placed on it has constant magnitude. If the angle between this force and the vertical is decreased, the frictional force between the surface and the body will

If pressure at half the depth of a lake is equal to 2/3 pressure at the bottom of the lake then what is the depth of the lake

The constant A in the Richardson-Dushman equation for tungsten is $60\times {10}^{4}A{m}^{-2}{K}^{-2}$ The work function of tungsten is 4.5 eV. A tungsten cathode having a surface area $2.0\times {10}^{-5}{m}^2$ is heated by the heater and the temperature becomes constant. Assuming that the cathode radiates like a blackbody, calculate the saturation current due to thermions. Take stefan constant$=6\times {10}^{-8}W{m}^{-2}{K}^{-4}.$ Assume that the termions take only a small fraction of th heat suplied.

A bar magnet takes $\frac{\pi }{10}$second to complete one oscillation in an oscillation magnetometer. The moment of inertia of the magnet about the axis of rotation is $1.2\times {10}^{-4}$ kg $m^3$ and the earth's horizontal magnetic field is $30\mu T$. Find the magnetic moment of the magnet.

How is an ammeter connected in a circuit?

How does a ammeter differ from an galvanometer?

In a simple Atwood machine, two unequal masses $m_1$ and $m_2$ are connected by a string going over a clamped light smooth pulley. In a typical arrangement (Figure) $m_1=300$ g and $m_2=600$g. The system is released from rest. (a) Find the distance travelled by the first block in the first two seconds. (b) Find the tension in the string. (c) Find the force exerted by the clamp on the pulley.

Three condensers C1, C2 and C3 are connected as shown to a battery. Which of them get charged by the battery?

A ball is dropped from the top of a building. The ball takes 0.5sec to fall past the 3m height of a window some distance from the top of the building. If the speed of the ball at the top and the bottom is $V_T$ and $V_B$, the establish a relationship between vb and vt take (g = 9.8m/s).

On a large tray of mass M, an ice cube of mass m, edge L is kept. If the ice melts completely, the centre of mass of the system comes down by

A thin circular ring of mass m and radius R is rotating about its axis with a constant angular velocity $\omega$. Two objects each of mass M are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity ${\omega }^1$ =

1. An object at an angle such that the horizontal range is 4 times of the maximum height .what is the angle projection of the object?

2. Football player hits the ball with speed 20 m per second with an angle 30 degree with respect too original direction .the goal post is a distance of 40 m from him. find out whether the ball reach the goal post.

3. If an object is thrown horizontally with an initial speed 10 M per second from the top of the building of height hundred metre. what is horizontal distance covered by the particle?

4. An object is thrown with initial speed 5 M per second set an angle of projection 30 .what is the height and range reached by the particle?

A spring of original length $x$ is extended to thrice its length. If the force constant of the spring is $k\text{N/m}$, its potential energy is