A train moves towards a stationary observer with speed \(34\, m/s\). The train sounds a whistle and its frequency registered by the observer is \(f_1\). If the speed of the train is reduced to \(17\, m/s\), the frequency registered is \(f_2\). If speed of sound is \(340\, m/s\), then the ratio \(f_1/f_2\) is

For a transistor to act as a switch, it must be operated in

A particle is moving in a circular path of radius \(a,\) with a constant velocity \(v\) as shown in the figure.The centre of circle is marked by \('C'\). The angular momentum from the origin \(O\) can be written as

Given below are two statements:
Statement I: An object moves from position \( r_{1} \) to position \( r_{2} \) under a conservative force field \( \vec{F} \). The work done by the force is \( W=-\int_{r_{1}}^{r_{2}}\vec{F}\cdot d\vec{r} \).
Statement II Any object moving from one location to another location can follow infinite number of paths. Therefore, the amount of work done by the object changes with the path it follows for a conservative force.
In the light of above statement, choose the correct answer from the options given below:

A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the figure. The radius of vessel is \(5\, cm\) and the angular speed of rotation is  \(\omega\; rad \,s^{-1}\). The difference in the height, \(h(\) in \(cm )\) of liquid at the centre of vessel and at the side will be

Which one of the following is not a measurable quantity ?

The angular width of the central maximum in a single slit diffraction pattern is \(60^o \) . The width of the slit is \(1\ \mu m\). The slit is illuminated by monochromatic plane waves. If another slit of same width is made near it, Young's fringes can be observed on a screen placed at  distance \(50\ cm\) from the slits. If the observed fringe width is \(1\ cm\), what is slit separation distance?.........\(\mu m\)
(i.e. distance between the centres of each slit. )

A string is wrapped around the rim of a wheel of moment of inertia \(0.40 \mathrm{kgm}^2\) and radius \(10 \mathrm{~cm}\). The wheel is free to rotate about its axis. Initially the wheel is at rest. The string is now pulled by a force of \(40 \mathrm{~N}\). The angular velocity of the wheel after \(10\) \(\mathrm{s}\) is \(\mathrm{x} \mathrm{rad} / \mathrm{s}\), where \(\mathrm{x}\) is _______.

Match the LIST-I with LIST-II

LIST-I	LIST-II
(A) Boltzmann constant	I. \(\mathrm{ML}^2 \mathrm{~T}^{-1}\)
(B) Coefficient of viscosity	II. \(\mathrm{MLT}^{-3} \mathrm{~K}^{-1}\)
(C) Planck's constant	III. \(\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\)
(D) Thermal conductivity	IV. \(\mathrm{ML}^{-1} \mathrm{~T}^{-1}\)

Choose the correct answer from the options given below :

A uniform thin bar of mass \(6 \,kg\) and length \(2.4\, meter\) is bent to make an equilateral hexagon. The moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of hexagon is ...... \(\times \,10^{-1} \,kg m ^{2}\)