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A body is executing S.H.M. When its displacement from the mean position is 4 cm and 5 cm, the corresponding velocity of the body is 10 cm/sec and 8 cm/sec. Then the time period of the body is

The Van Der Waal’s equation of state for some gases can be expressed as: $(P+\frac{a}{V^2})(V-b)=RT$ Where $P$ is the pressure, $V$ is the molar volume and $T$ is the absolute temperature of the given sample of gas and $a,b$ and $R$ are constants.

The dimensions of constant $b$ are

If polar ice caps melt, then the angular velocity of rotation of earth

A thin lens made of a material of refractive index ${\mu }_2$, has a medium of refractive index ${\mu }_1$ on one side and a medium of refractive index ${\mu }_2$ on the other side. The lens is biconvex and the two radii of curvature have equal magnitude R. A beam of light travelling parallel to the principal axis is incident on the lens. Where will the image be formed if the beam is incident from

(a) The medium ${\mu }_1$, and

(b) From the medium ${\mu }_3$ ?

Sound waves from a loudspeaker spread nearly uniformly in all directions if the wavelength of the sound is much larger than the diameter of the loudspeaker. (a) Calculate the frequency for which the wavelength of sound in air is ten times the diameter of the speaker if the diameter is 20 cm. (b) Sound is essentially transmitted in the forward direction if wavelength is much shorter than the diameter of the speaker. Calculate the frequency at which the wavelength of the sound is one tenth of the diameter of the speaker. described above. Take the speed of sound to be $340m{s}^{-1}$.

Unpolarized light with an intensity of $I_0=16\frac{W}{m^2}$ is incident on a pair of polarizers. The first polarizer has its transmission axis aligned at ${50}^{\circ }$ from the vertical. The second polarizer has its transmission axis aligned at ${20}^{\circ }$ from the vertical.

What is the intensity of the light when it emerges from the first polarizer?

Two equilateral triangular plates are joined together to form the following figure. Density of plate $A$ is $3$ times that of plate $B$. If $COM$ lies inside the plate $A$ at a distance $h=\sqrt{3}\text{m}$ from their common side, find out the length of side of each triangular plate.

The wavelength of light in two liquids 'x' and 'y' is 3500 $\stackrel{\circ }{A}$ and 7000 $\stackrel{\circ }{A}$, then the critical angle of x relative to y will be

A uniform chain of length l and mass m overhangs a smooth table with its two third part lying on the table. The kinetic energy of the chain as it completely slips off the table is

A particle is projected upward from the surface of earth (radius = R) with a speed equal to the orbital speed of a satellite near the earth's surface. The height to which it would rise is

A block of mass 0.1 kg is held against a wall applying a horizontal force of 5 N of the block. If the coefficient of friction between the block and the wall is 0.5, the magnitude of the frictional force acting on the block is

A simple pendulum is released from $A$ as shown. If $M$ and $l$ represent the mass of the bob and length of the pendulum respectively, the gain in kinetic energy at B is

A purse at radius 2.00 m and a wallet at radius 3.00 m travel in uniform circular motion on the floor of a merry-go-round as the ride turns. They are on the same radial line. At one instant, the acceleration of the purse is (2.00 m/ $s^2$)$\hat{i}$ + (4.00 m/ $s^2$)$\hat{j}$ . At that instant and in unit-vector notation, what is the acceleration of the wallet? IIT JEE- 2001

If a particle moves in a circle describing equal angles in equal times, its velocity vector

If a solid cylinder rolls up along a inclined plane with an initial velocity v. It will rise up to a height h equal to

A ball of mass 0.1 Kg. is whirled in a horizontal circle of radius 1 m. by means of a string at an initial speed of 10 R.P.M. Keeping the radius constant, the tension in the string is reduced to one quarter of its initial value. The new speed is

If the flux of magnetic induction through a coil of resistance R and having n turns changes from ${\Phi }_1$ to ${\Phi }_2$, then the magnitude of the charge that passes through the coil is

An ideal massless spring $S$ can be compressed by $1m$ by a force of $100N$ in equilibrium. The same spring is placed at the bottom of a frictionless inclined plane at ${30}^{\circ }$ to the horizontal. A $10kg$ block $M$ is released from rest at the top of the incline and is brought to rest momentarily after compressing the spring by $2m$. If $g=10m/s^2$, what is the speed of mass just before it touches the spring?

A compound $M{X}_2$ has observed and normal molar masses 65.6 and 164 respectively. Calculate the apparent degree of ionization of $M{X}_2$

A parallel beam of monochromatic light of wavelenght $\lambda$ is used in a Young's double slit experiment. The slits are separated by a distance d and the screen is placed parallel to the plane of the slits. The incident beam makes an angle $\theta =si{n}^{-1}\left(\frac{\lambda }{2d}\right)$ with the normal to the plane of the slits. A transparent sheet of refractive index. ${}^{\prime }{\mu }^{\prime }$ and thickness $t=\frac{\lambda }{2(\mu -1)}$ is introduced infront of one of the slit. Find the intensity at the geometrical centre.

A proton is released from position near to positive plate. It reaches to opposite plate in time $t_1$, now one $\alpha$ particle is released & it reaches to opposite plate in time $t_2$, then $t_1:t_2$

The sum of number of neutrons and protons in tritium is:

A body travels for $15\text{sec}$ starting from rest with constant acceleration. If it travels $S_1,S_2$ and $S_3$ in the first 5 seconds, second 5 seconds and next five seconds respectively. The relation between $S_1,S_2$ and $S_3$ is

The rms speed of oxygen molecules in a gas is v. If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms, the rms speed will become

The diode used in the circuit shown in the figure has a constant voltage drop of 0.5 V at all currents and a maximum power rating of 100 milliwatts. What should be the value of the resistor R, connected in series with the diode for obtaining maximum current

The de-Broglie wavelength associated with an electron in the 3rd orbit is nearly

It is not possible to write directly on blotting paper or newspaper with ink pen

When a current of $5mA$ is passed through a galvanometer having a coil of resistance $15\Omega$, it shows full scale deflection. The value of the resistance to be put in series with the galvanometer to convert it into a voltmeter of range $0-10V$ is

A cylinder rolls without slipping down an inclined plane, the number of degrees of freedom it has, is

A TV tower has a height of $100m$. How much population is covered by the TV broadcast if the average population density around the tower is $1000k{m}^{-2}$?

The motion of a particle executing SHM is given by x = 0.01 sin 100, where x is in metre and time t is in second. The time period is

A convex mirror of focal length f forms an image which is $\frac{1}{n}$ times the object. The distance of the object from the mirror is:

In the circuit shown in figure the base current $I_B$ is 10 $\mu$ A and the collector is 5.2 mA. The value of $V_{BE}$ is

If $E$ is the electric field intensity of an electrostatic field, then the electrostatic energy density is proportional to

A galvanometer of resistance 50 $\Omega$ gives a full scale deflection for a current $5\times {10}^{-4}A$. The resistance that should be connected in series with the galvanometer to read 3 V is

A potential difference of $2\text{V}$ is applied between the opposite faces of a Ge crystal plate of area $1{\text{cm}}^2$ and thickness $0.5\text{mm}$. If the concentration of electrons in Ge is $2\times {10}^{19}/m^3$ and mobilities of electrons and holes are $0.36\frac{m^2}{\text{volt -sec}}$ and $0.14\frac{m^2}{\text{volt -sec}}$ respectively, then the current flowing through the plate will be

A uniform rope of length 12 m and mass 6 kg hangs vertically from a rigid support. A block of mass 2 kg is attached to the free end of the rope. A transverse pulse of wavelength 0.06 m is produced at the lower end of the rope. What is the wavelength of the pulse when it reaches the top of the rope.

A wire loop enclosing a semicircle of radius $R$ is located on the boundary of uniform magnetic field $B$. At time $t=0$, the loop is set into motion with constant angular accleration $\alpha$ about an axis passing through $O$ and is perpendicular to semicircle. The clockwise emf direction is taken to be positive. The modulus of variation of emf as a function of time is ($0<\theta <\pi$)

Consider the refraction of light ray as shown in the figure below. Incident ray is rotating with constant angular velocity 2 rad/sec. What is the angular velocity of refracted ray, when the angle of incidence becomes ${30}^{\circ }$? (Given $\frac{n_1}{n_2}=\sqrt{3}$)

Two charged particles having charge $2.0\times {10}^{-8}C$ each are joined by an insulating string of length 1 ma nd the system is kept on a smooth horizontal table. Find he tension in the string.
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Let LL’ be the latus rectum through the focus S of a hyperbola and A’ be the farther vertex of the conic.If $\Delta$ A’ LL’ is equilateral then its eccentricity e =

A boy riding on his bike is going towards east at a speed of $4\sqrt{2}m{s}^{-1}$. At a certain point he produces a sound pulse of frequency 1650 Hz that travels in air at a speed of $334m{s}^{-1}$. A second boy stands on the ground ${45}^{\circ }$ south of east from him. Find the frequency of the pulse as received by the second boy.