AIEEE 2003

Let \(\overrightarrow F\) be the force acting on a particle having position vector \(\overrightarrow r ,\) and \(\overrightarrow \tau\) be the torque of this force about the origin. Then

A particle performing uniform circular motion has angular frequency is doubled & its kinetic energy halved, then the new angular momentum is

A circular disc \(X\) of radius \(R\) is made from an iron plate of thickness \(t,\) and another disc \(Y\) of radius \(4\) \(R\) is made from an iron plate of thickness \({t \over 4}.\) Then the relation between the moment of inertia $${I...

The displacement of particle varies according to the relation
\(x=4\)\(\left( {\cos \,\pi t + \sin \,\pi t} \right).\) The amplitude of the particle is

Two particles \(A\) and \(B\) of equal masses are suspended from two massless springs of spring of spring constant \({k_1}\) and \({k_2}\), respectively. If the maximum velocities, during oscillation, are equal, the ratio of amplitude of $...

A body executes simple harmonic motion. The potential energy \((P.E),\) the kinetic energy \((K.E)\) and total energy \((T.E)\) are measured as a function of displacement \(x.\) Which of the following statements is true ?

The length of a simple pendulum executing simple harmonic motion is increased by \(21\%\). The percentage increase in the time period of the pendulum of increased length is

A mass \(M\) is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes \(SHM\) of time period \(T.\) If the mass is increased by \(m.\) the time period becomes $${{5T} \over 3}$...

The physical quantities not having same dimensions are

Dimensions of \({1 \over {{\mu _0}{\varepsilon _0}}}\), where symbols have their usual meaning, are

To demonstrate the phenomenon of interference, we require two sources which emit radiation

A metal wire of linear mass density of \(9.8\) \(g/m\) is stretched with a tension of \(10\) \(kg\)-\(wt\) between two rigid supports \(1\) metre apart. The wire passes at its middle point between the poles of a permanent magnet, and it vib...

The displacement \(y\) of a wave travelling in the \(x\)-direction is given by
\($y = {10^{ - 4}}\,\sin \left( {600t - 2x + {\pi \over 3}} \right)\,\,metres\)$
where \(x\) is expressed in metres and \(t\) in seconds. The speed of the wave...

A tuning fork of known frequency \(256\) \(Hz\) makes \(5\) beats per second with the vibrating string of a piano. The beat frequency decreases to \(2\) beats per second when the tension in the piano string is slightly increased. The freque...

A spring of spring constant \(5 \times {10^3}\,N/m\) is stretched initially by \(5\) \(cm\) from the unstretched position. Then the work required to stretch it further by another \(5\) \(cm\) is

A wire suspended vertically from one of its ends is stretched by attaching a weight of \(200N\) to the lower end. The weight stretches the wire by \(1\) \(mm.\) Then the elastic energy stored in the wire is

A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time \('t'\) is proportional to