In a dilute gas at pressure \(P\) and temperature \(T\), the mean time between successive collisions of a molecule varies with \(T\) as

In the given figure, two wheels \(P\) and \(Q\) are connected by a belt \(B\). The radius of \(P\) is three times as that of \(Q\). In case of same rotational kinetic energy, the ratio of rotational inertias \(\left(\frac{{I}_{1}}{{I}_{2}}\right)\) will be \({x}: 1\). The value of \({x}\) will be \(.....\, .\)

A particle executes \(S.H.M.,\) the graph of velocity as a function of displacement is :-

An experiment is performed to obtain the value of acceleration due to gravity \(g\) by using a simple pendulum of length \(L\). In this experiment time for \(100\, oscillations\) is measured by using a watch of \(1\, second\) least count and the value is \(90.0\, seconds\). The length \(L\) is measured by using a meter scale of least count \(1\, mm\) and the value is \(20.0\, cm\). The  error in the determination of \(g\) would be  ........... \(\%\)

A simple pendulum made of a bob of mass \(m\) and a metallic wire of negligible mass has time period \(2s\) at  \(T = 0\,^oC\) . If the temeprature of the wire is increased and the corresponding change in its time peirod is plotted against its temperature, the resulting graph is a line of slope \(S\). If the coefficient of linear expansion of metal is \(\alpha \) then the value of  \(S\) is

The parameter that remains the same for molecules of all gases at a given temperature is _______.

A block takes \(t\) time to slide down a plane inclined at \(45°\) to the horizontal. If the surface is made smooth (frictionless), the block takes time \(\dfrac{t}{2}\) to slide down the plane. The coefficient of friction between the block and the inclined plane is \(\left(\dfrac{\alpha}{100}\right)\). The value of \(\alpha\) is __________.

A plane electromagnetic wave of frequency \(35\  \mathrm{MHz}\) travels in free space along the \(\mathrm{X}\)-direction. At a particular point (in space and time) \(\overrightarrow{\mathrm{E}}=9.6\  \hat{\mathrm{j}} \mathrm{V} / \mathrm{m}\). The value of magnetic field at this point is _______.

A thin convex lens made from crown glass \(\left( {\mu = \frac{3}{2}} \right)\) has focal length \(f\). When it is measured in two different liquids having refractive indices \(\frac{4}{3}\) and \(\frac{5}{3}\) it has the focal lengths \(f_1\) and \(f_2\) respectively. The correct relation between the focal lengths is: