If the moment of inertia of a uniform solid cylinder about the axis of the cylinder is \(\frac{1}{n}\) times its moment of inertia about an axis passing through its midpoint and perpendicular to its length, then the ratio of the length and radius of the cylinder is

Which of the following statement is incorrect?

A message signal of frequency $15 \mathrm{kHz}$ is used to modulate a carrier of frequency $v_c$. If the side bands produced are $1515 \mathrm{kHz}$ and $1485 \mathrm{kHz}$, then $v_c$ is

A proton, a deuteron (nucleus of \({ }_1 \mathrm{H}^2\) ) and an \(\alpha\)-particle with same kinetic energy enter a region of uniform magnetic field moving at right angles to the field. The ratio of the radii of their circular paths is :

Statement (I) : The slope of kinetic energy-displacement curve of a body in motion will be directly proportional to its acceleration. Statement (II) : From a height of \(15 \mathrm{~m}\) a ball is projected vertically upwards with a velocity of \(30 \mathrm{~m} / \mathrm{s}\). If the ball rises to the same height after hitting the ground, the loss of its energy on hitting the ground is \(30 \%\). Statement (III) : The velocity acquired by a body of mass ' \(m\) ' after travelling a fixed distance from rest under the action of a constant force is directly proportional to mass ' \(\mathrm{m}\) '. Which of the following is correct?

In a photoelectric experiment, the slope of the graph drawn between stopping potential along y -axis and frequency of incident radiation along x -axis is (Planck's constant \(=6.6 \times 10^{-34} \mathrm{Js}\) )

For the circuit shown in the figure, calculate the resistance between the points \(A\) and \(\mathrm{B}\).

Two bar magnets \(A\) and \(B\) are placed one over the other and are allowed to vibrate in a vibration magnetometer. They make 20 oscillations per minute when the similar poles of \(A\) and \(B\) are on the same side, while they make 15 oscillations per minute when their opposite poles lie on the same side. If \(M_A\) and \(M_B\) are the magnetic moments of \(A\) and \(B\) and if \(M_A>M_B\), the ratio of \(M_A\) and \(M_B\) is

The ratio of the areas of cross sections of three wires in 1:2:3 and the ratio of the Young's modulii of their materials is \(3: 2: 1\). If the three wires are of same length and same stretching force is applied to the three wires, then the ratio of the elongations of the three wires is

Statement (I) : An object subjected to velocities \(\overrightarrow{v_1}\) and \(\overrightarrow{v_2}\) has a resultant velocity with magnitude \(|\vec{v}|=\left|\overrightarrow{v_1}\right|+\left|\overrightarrow{v_2}\right|\).
Statement (II) : The magnitude of displacement is either less or equal to the path length of an object between two points.
Statement (III) : The instantaneous acceleration is the limiting value of the average acceleration as the time interval approaches zero.
Which of the following is correct?

A pendulum has a time period \(\mathrm{T}\) in air. When it is made to oscillate in water its time period is \(\sqrt{2} \mathrm{~T}\). Then the relative density of the material of the bob of the pendulum is (neglect damping)

The sensitivity of a galvanometer that measures current is decreased by \(\frac{1}{40}\) times by using shunt resistance of \(10 \Omega\). Then, the value of the resistance of the galvanometer is

Two electric charges \(+2 \mu \mathrm{C}\) and \(-4 \mu \mathrm{C}\) are separated by a distance \(3 \mathrm{~m}\) in air. At a point \(\mathrm{P}\) located on the line joining the two charges and in between them, the electric potential is zero. Then the electric field at a point \(\mathrm{P}\left(\right.\) in \(\left.\mathrm{NC}^{-1}\right)\) is