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The superposing waves are represented by the following equations :

$y_1=5sin2\pi (10t-0.1x),y_2=10sin2\pi (20t-0.2x)$

Ratio of intensities $\frac{I_{max}}{I_{min}}$ will be

[AIIMS 1995; KCET 2001]

The maximum speed and acceleration of a particle executing simple harmonic motion are $10cm{s}^{-1}$ and $50cm{s}^{-2}$. Find the positions (s) of the particle when the speed is $8cm{s}^{-1}$.

A ball is dropped vertically from a height $10\text{m}$ above the ground. It hits the ground and bounces up vertically to a height of $5\text{m}$. Neglecting subsequent motion and air resistance, which of the following options correctly represents the variation of its velocity $v$ with height $h$ above the ground.

A siren placed at a railway platform is emitting sound of frequency 5 kHz. A passenger sitting in a moving train A, records a frequency of 5.5 kHz while the train approaches the siren. During his return journey in a different train B, he records a frequency of 6.0 kHz while approaching the same siren. The ratio of the velocity of train B to that of train A is

A parallel-plate capacitor is being charged. The displacement current across an area in the region between the plates and parallel to it is equal to

What should be the length of a dipole antenna for a carrier wave of frequency 6x 10⁸ Hz?

Find the rate of heat flow through a cross section of the rod shown in figure $({\theta }_2>{\theta }_1)$. Thermal conductivity of the material of the rod is K.

A TV tower has a height of 400m at a given place. If the radius of the earth is 6400 km, its coverage range is:

A particle is executing S.H.M. If its amplitude is 2 m and periodic time 2 seconds, then the maximum velocity of the particle will be

A railroad car of mass M is at rest on friction less rails when a man of mass m starts moving on the car towards the engine.If the car recoils with a speed v backward on the rails,with what velocity is the man approaching the engine?

Two long, straight wires, each carrying a current of 5 A, are placed along the x- and y-axes respectively. The currents point along the positive directions of the axes. Find the magnetic fields at the points (a) (1 m,1 m), (b) (-1 m, 1 m), (c) (-1 m,-1 m) and (d) (1 m,-1 m).

A stone is projected from the ground with a velocity $50\text{m/s}$ at an angle of ${30}^{\circ }$. It crosses a wall after 3 sec. How far beyond the wall the stone will strike the ground ($g=10{\text{m/s}}^2$)

Comprehension Type: A uniform thin cylindrical disk of mass M ad radius R is attached to two identical mass less springs of springs constant k which are fixed to the wall as show in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance d from its center. The axle is mass less and both the springs and the axle are in horizontal plane. The un-stretched length of each springs is L. The disk is initially at its equilibrium position with its center of mass (CM) at a distance L from the wall. The disk rolls without slipping with velocity $\overrightarrow{(}V{)}_0=V_0\hat{i}$ The coefficient of friction is $\mu$.

The net external force acting on the disk when its centre of mass is at displacement x with respect to its equilibrium position is

Find the moment of inertia of a uniform rod of mass $M$ and length $L$, about $OA$ {$PQ$ makes an angle of ${30}^{\circ }$ with $OA$ as shown in figure}.

A simple pendulum of length l is suspended through the ceiling of an elevator. Find the time period of small oscillations if the elevator (a) is going up with an acceleration $a_0$ (b) is going down with an acceleration $a_0$ and (c) is moving with a uniform velocity.

In the arrangement shown in figure the ends P and Q of an unstretchable string move downwards with uniform speed U. Pulleys A and B are fixed. Mass M moves upwards with a speed

A photographic plate records suffciently intense lines when it is exposed for 12 s to a source of 10 W. source radiating the light of same colour to get equal intense lines ?

A dip circle is adjusted so that its needle moves freely in the magnetic meridian. In this position, the angle of dip is
​${40}^{\circ }$. Now the dip circle is rotated so that the plane in which the needle moves makes an angle of ​${30}^{\circ }$ with the magnetic meridian. In this position the needle will dip by an angle

What will be de-Broglie wavelength of an electron moving with a velocity of $1.2\times {10}^{5}m{s}^{-1}$

Two waves of equal frequencies moving in the same direction have their amplitudes in the ratio $7:5$. They are superimposed on each other. Find the ratio of maximum to minimum intensity of the resultant wave.

Dimentional formula of permeability of free space ${\mu }_0$ is given by

A red LED emits light at $0.1$ Watt uniformly around it. The amplitude of the electric field of the light at a distance of $1m$ from the diode is

A block of mass m is pushed against α spring of spring constant k fixed at one end to a wall. The block can slide on α frictionless table as shown in figure. The natural length of the spring is L₀ and it is compressed to half its natural length when the block is released. Find the velocity of the block as α function of its distance x from the wall (for $x>L_0$).

Calculate the average velocity of Sulphur dioxide molecule at ${427}^{\circ }$C.

A solid cylinder is released from rest from the top of an inclined plane of inclination $\theta$ and length ${}^{\prime }{l}^{\prime }$. If the cylinder rolls without slipping, then find it's speed when it reaches the bottom of inclined plane.

What can you say about the tangential and normal components of acceleration if the direction of velocity of a body is changing?

A solid sphere of mass $M$ and radius $R$ is rotating about its diameter. A hollow sphere of same mass and same external radius is also rotating with an angular speed twice that of solid sphere. The ratio of their kinetic energies of rotation $(E_S:E_H)$ will be

A light source of wavelenght ${}^{\prime }{\lambda }^{\prime }$ illuminates on a metal surface, a photoelectron of Kinetic energy $1eV$ is emitted. The another light source of wavelength $\frac{\lambda }{3}$ ejects photo electron from the same metal surface with Kinetic energy is $4eV$, the value of work function is

Due to capillary action, a liquid will rise in a tube, if the angle of contact is

A shell is fired from a cannon with velocity v m/sec at an angle: $\theta$ with the horizontal direction. At the highest point in its path it explodes into two pieces of equal mass. One of the pieces retraces its path to the cannon and the speed in m/sec of the other piece immediately after the explosion is

which of the fpollowing graphs show the variation of Potential Energy of a body if it is taken to a height h and dropped from there?

The ratio among most probable velocity, mean velocity and root mean square velocity is given by

For the damped oscillator system shown with m = 250g, k = 85 N/m, and b = 70 g/s, what is the ratio of the oscillation amplitude at the end of 20 cycles to the initial oscillation amplitude?

The network shown in the figure is part of a complete circuit. If at a certain instant, the current I is 5 A and it is decreasing at a rate of ${10}^{3}A{s}^{-1}$ then $V_B-V_A$ equals

A steel wire has length $l=2\text{m}$, radius $r=1\text{mm}$ and Young's modulus of elasticity $Y=2\times {10}^{11}{\text{Nm}}^{-2}.$ A sphere of mass $1\text{kg}$ is attached to one end of the wire and is whirled in a vertical circle with an angular speed of $2\text{rev/s}$. When the sphere is at the lowest point of the vertical circle, the elongation of the wire is nearly
[Assume , $g=10{\text{ms}}^{-2})$ ]

At time $t=0,$ equation of a wave pulse is $y(x,0)=\frac{5}{3+(x-4{)}^2}$ and at $t=2s$, equation of the same wave pulse is $y(x,2)=\frac{5}{3+(x+8{)}^2}$. Here, $y$ is in $\text{mm}$, $x$ is in $\text{m}$ and $t$ is in $\text{sec}$. The wave speed is

A larger tank with a nozzle attached contains three immiscible fluids as shown in figure. Assuming that the changes in $h_1,h_2$ and $h_3$ are negligible, the discharge velocity at this instant is

The change in internal energy of a system that has absorbed $2\text{kcal}$ of heat and does $500\text{J}$ of work is

A block of mass $1kg$ lies on horizontal surface in a truck. The coefficient of static friction between the block and the surface is ${\mu }_s=0.6$. If the acceleration of the truck is $5m/s^2$, the friction force acting on the block is