IIT-JEE 2005 Mains

Highly energetic electrons are bombarded on a target of an element containing 30 neutrons. The ratio of radii of nucleus to that of Helium nucleus is \((14)^{\frac{1}{3}}\). Find
(A) Atomic number of the nucleus;
(B) the frequency of $$\mat...

In the given circuit, the switch S is closed at time \(t=0\). The charge Q on the capacitor at any instant t is given by \(Q(t)=Q_0(1-e^{-\alpha t})\). Find the value of Q\(_0\) and \(\alpha\) in terms of given parameters shown in the circu...

An unknown resistance X is to be
determined using resistances R\(_1\), R\(_2\) or R\(_3\). Their corresponding null points are A, B
and C. Find which of the above will give the
most accurate reading and why ?

The potential energy of a particle of mass m
is given by
$$\mathrm{U}(x)=\left\{\begin{array}{cc}\mathrm{E}_{0} & 0 \leq x \leq 1 \\ 0 & x>1\end{array}\right.$$
\(\lambda_{1}\) and \(\lambda_{2}\) are the de Broglie wavelengths of the part...

A long solenoid of radius a and number of turns per unit length \(n\) is enclosed by cylindrical shell of radius R, thickness \(d\) \((d < < R)\) and length L. A variable current \(\mathrm{I}=\mathrm{I}_{0} \sin \omega t\) flows through the...

A conducting liquid bubble of radius \(a\) and thickness \(t(t < < a)\) is charged to potential V. If the bubble collapses to a droplet, find the potential on the droplet.

What will be the minimum angle of incidence such that the total internal reflection occurs on both the surfaces?

Two identical prisms of refractive index \(\sqrt{3}\) are kept as shown in the figure. A light ray strikes the first prism at face AB. Find
(A) the angle of incidence so that the
emergent ray from the first prism has
minimum deviation;
(...

A cylinder of mass \(1 \mathrm{~kg}\) is given heat of \(20000 \mathrm{~J}\) at atmospheric pressure. If initially temperature of cylinder is \(20^{\circ} \mathrm{C}\), find
(A) The final temperature of the cylinder;
(B) The work done by th...

In a moving coil galvanometer, torque on the coil can be expressed as \(\tau=k i\), where \(i\) is current through the wire and \(k\) is constant. The rectangular coil of the galvanometer having numbers of turns \(\mathrm{N}\), area $$\math...

A U-tube is rotated about one of its limbs with an angular velocity \(\omega\). Find the difference in height \(\mathrm{H}\) of the liquid (density \(\rho\) ) level, where the diameter of the tube is \(d < <\mathrm{L}\).

A wooden log of mass M and length L is
hinged by a frictionless nail at O; a bullet
of mass m strikes with velocity \(v\) and sticks
to it. Find angular velocity of the system
immediately after the collision about O.

A cylinder of mass m and radius R rolls
down on an inclined plane of inclination \(\theta\).
Calculate the linear acceleration of axis of
cylinder.

Two identical ladders, each of mass M and
length L are resting on the rough horizontal
surface as shown in the figure. A block of
mass \(m\) hangs from P. If the system is in
equilibrium, find the magnitude and the
direction of frictio...

A small body attached to one end of a vertically hanging spring is performing SHM about its mean position with angular frequency \(\omega\) and amplitude \(a\). If at a height \(y^{\prime}\) from the mean position, the body gets detached fr...

The side of a cube is measured by vernier
callipers (10 divisions of a vernier scale
coincide with 9 divisions of main scale,
where 1 division of main scale is 1 mm). The
main scale reads 10 mm and first division of
vernier scale coinc...

A whistling train approaches a junction. An
observer standing at the junction observes
the frequency to be 2.2 kHz and 1.8 kHz
of the approaching and the receding train.
Find the speed of the train (speed of sound
= 300 m/s).

A transverse harmonic disturbance is
produced in a string. The maximum
transverse velocity is 3 m/s and the maximum
transverse acceleration is 90 m/s\(^2\)
. If the wave velocity is 20 m/s, then find the waveform.