The mean free path and the average speed of oxygen molecules at 300 K and 1 atm are \(3 \times 10^{-7} \mathrm{~m}\) and \(600 \mathrm{~m} / \mathrm{s}\) respectively. Find the frequency of its collisions.

The magnetic field of a plane electromagnetic Wave is \(\overrightarrow{ B }=3 \times 10^{-8} \sin [200 \pi( y + ct )] \hat{ i }\, T\) Where \(c=3 \times 10^{8} \,ms ^{-1}\) is the speed of light. The corresponding electric field is

The equation of a wave travelling on a string is \(\mathrm{y}=\sin [20 \pi \mathrm{x}+10 \pi \mathrm{t}]\), where x and t are distance and time in SI units. The minimum distance between two points having the same oscillating speed is :

In an experiment to find out the diameter of wire using screw gauge, the following observation were noted. \((a)\) Screw moves \(0.5\,mm\) on main scale in one complete rotation \((b)\) Total divisions on circular scale \(=50\) \((c)\) Main scale reading is \(2.5\,mm\) \((d)\) \(45^{\text {th }}\) division of circular scale is in the pitch line \((e)\) Instrument has \(0.03 \;mm\) negative error Then the diameter of wire is \(...........\,mm\)

A 20 m long uniform copper wire held horizontally is allowed to fall under the gravity ( \(g =10 m / s ^2\) ) through a uniform horizontal magnetic field of 0.5 Gauss perpendicular to the length of the wire. The induced EMF across the wire it travells a vertical distance of 200 m is ___________ mV .

Given below are two statements: statement\(-I\) : The reactance of an ac circuit is zero. It is possible that the circuit contains a capacitor and an inductor. Statement\(-II\) : In \(ac\) circuit, the average power delivered by the source never becomes zero. In the light of the above statements, choose the correct answer from the options given below

A balloon and its content having mass \(M\) is moving up with an acceleration ' \(a\) '. The mass that must be released from the content so that the balloon starts moving up with an acceleration ' \(3 a^{\prime}\) will be
(Take ' g ' as acceleration due to gravity)

A cylindrical block of mass M and area of cross section A is floating in a liquid of density \(\rho\) and with its axis vertical. When depressed a little and released the block starts oscillating. The period of oscillation is _________ .

The speed of light in media \('A'\) and \('B'\) are \(2.0 \times\) \(10^{10} \,cm / s\) and \(1.5 \times 10^{10} \,cm / s\) respectively. A ray of light enters from the medium \(B\) to \(A\) at an incident angle ' \(\theta\) '. If the ray suffers total internal reflection, then

A particle moves in one dimension from rest under the influence of a force that varies with the distance traveled by the particle as shown in the figure. The kinetic energy of the particle after it has traveled \(3\, m\) is ................ \(\mathrm{J}\)

A cord is wound round the circumference of wheel of radius \(r\). The axis of the wheel is horizontal and moment of inertia about it is \(I\). A weight \(mg\) is attached to the end of the cord and falls from rest. After falling through a distance \(h\), the angular velocity of the wheel will be

A compound microscope consists of an objective lens of focal length \(1 \,cm\) and an eye piece of focal length \(5 \,cm\) with a separation of \(10 \,cm\) The distance between an object and the objective lens, at which the strain on the eye is minimum is \(\frac{ n }{40}\, cm .\) The value of \(n\) is\(....\)