AIEEE 2003

A magnetic needle lying parallel to a magnetic field requires \(W\) units of work to turn it through \({60^ \circ }.\) The torque needed to maintain the needle in this position will be :

A particle of charge \(- 16 \times {10^{ - 18}}\) coulomb moving with velocity \(10m{s^{ - 1}}\) along the \(x\)-axis enters a region where a magnetic field of induction \(B\) is along the \(y\)-axis, and an electric field of magnitude $${...

A particle of mass \(M\) and charge \(Q\) moving with velocity \(\overrightarrow v\) describe a circular path of radius \(R\) when subjected to a uniform transverse magnetic field of induction \(B.\) The network done by the field when the ...

A boy playing on the roof of a 10 m high building throws a ball with a speed of 10 m/s at an
angle of \(30^\circ\) with the horizontal. How far from the throwing point will the ball be at the height
of 10 m from the ground?
$$\left[ {g = 1...

A car, moving with a speed of 50 km/hr, can be stopped by brakes after at least 6 m. If the
same car is moving at a speed of 100 km/hr, the minimum stopping distance is

The co-ordinates of a moving particle at any time 't' are given by x = \(\alpha\)t3 and y = βt3. The speed to the particle at time 't' is given by

According to Newton's law of cooling, the rate of cooling of a body is proportional to \({\left( {\Delta \theta } \right)^n},\) where \({\Delta \theta }\) is the difference of the temperature of the body and the surrounding, and \(n\) is e...

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