AIEEE 2007

A block of mass \(m\) is connected to another block of \(mass\) \(M\) by a spring (massless) of spring constant \(k.\) The block are kept on a smooth horizontal plane. Initially the blocks are at rest and the spring is unstretched. Then a c...

Two identical conducting wires \(AOB\) and \(COD\) are placed at right angles to each other. The wire \(AOB\) carries an electric current \({I_1}\) and \(COD\) carries a current \({I_2}\). The magnetic field on a point lying at a distance $...

A current \(I\) flows along the length of an infinitely long, straight, thin walled pipe. Then

A long straight wire of radius \(a\) carries a steady current \(i.\) The current is uniformly distributed across its cross section. The ratio of the magnetic field at \(a/2\) and \(2a\) is

A charged particle moves through a magnetic field perpendicular to its direction. Then

A charged particle with charge \(q\) enters a region of constant, uniform and mutually orthogonal fields \(\overrightarrow E\) and \(\overrightarrow B\) with a velocity \(\overrightarrow v\) perpendicular to both \(\overrightarrow E\) a...

The velocity of a particle is v = v0 + gt + ft2. If its position is x = 0 at t = 0, then its displacement after unit time (t = 1) is

For the given uniform square lamina \(ABCD\), whose center is \(O,\)

A round uniform body of radius \(R,\) mass \(M\) and moment of inertia \(I\) rolls down (without slipping) an inclined plane making an angle \(\theta\) with the horizontal. Then its acceleration is

Angular momentum of the particle rotating with a central force is constant due to

The displacement of an object attached to a spring and executing simple harmonic motion is given by \(x = 2 \times {10^{ - 2}}\) \(cos\) \(\pi t\) metre. The time at which the maximum speed first occurs is

Two springs, of force constant \({k_1}\) and \({k_2}\) are connected to a mass \(m\) as shown. The frequency of oscillation of the mass is \(f.\) If both \({k_1}\) and \({k_2}\) are made four times their original values, the frequency of os...

A point mass oscillates along the \(x\)-axis according to the law \(x = {x_0}\,\cos \left( {\omega t - \pi /4} \right).\) If the acceleration of the particle is written as \(a = A\,\cos \left( {\omega t + \delta } \right),\) then

A particle of mass \(m\) executes simple harmonic motion with amplitude a and frequency \(v.\) The average kinetic energy during its motion from the position of equilibrium to the end is

In a Young's double slit experiment the intensity at a point where the path difference is \({\lambda \over 6}\) ( \(\lambda\) being the wavelength of light used ) is \(I\). If \({I_0}\) denotes the maximum intensity, \({I \over {{I_0}}}\)...

A sound absorber attenuates the sound level by \(20\) \(dB\). The intensity decreases by a factor of

A \(2\) \(kg\) block slides on a horizontal floor with a speed of \(4m/s.\) It strikes a uncompressed spring, and compress it till the block is motionless. The kinetic friction force is \(15N\) and spring constant is \(10, 000\) \(N/m.\) Th...

A particle is projected at \(60^\circ\) to the horizontal with a kinetic energy K. The kinetic energy at the
highest point is