Air of density \(1.2\,kg\,m^{-3}\) is blowing across the horizontal Wings of an aeroplane in such a way that its speeds above and below the wings are \(150\,ms^{-1}\) and \(100\,ms^{-1}\), respectively. The pressure difference between the upper and lower sides of the Wings, is ........ \(Nm^{-2}\)

A spherical body of mass \(100 \mathrm{~g}\) is dropped from a height of \(10 \mathrm{~m}\) from the ground. After hitting the ground, the body rebounds to a height of \(5 \mathrm{~m}\). The impulse of force imparted by the ground to the body is given by : _______. (given \(\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^2\) )

Hot water cools from \(60\,^oC\) to \(50\,^oC\) in the first \(10\,minutes\) and to \(42\,^oC\) in the next \(10\,minutes.\) The temperature of the surroundings is ...... \(^oC\)

Diameter of the objective lens of a telescope is \(250\, cm\). For light of wavelength \(600\, nm\). Coming from a distant object, the limit of resolution of the telescope is close to

There are two identical chambers, completely thermally insulated from surroundings. Both chambers have a partition wall dividing the chambers in two compartments. Compartment \(1\) is filled with an ideal gas and Compartment \(3\) is filled with a real gas. Compartments \(2\) and \(4\) are vacuum . A small hole (orifice) is made in the partition walls and the gases are allowed to expand in vacuum Statement \(-1\) : No change in the temperature of the gas takes place when ideal gas expands in vacuum. However, the temperature of real gas goes down (cooling) when it expands in vacuum Statement \(-2\) : The internal energy of an ideal gas is only kinetic. The internal energy of a real gas is kinetic as well as potential

Sixty four rain drops of radius 1 mm each falling down with a terminal velocity of \(10 cm / s\) coalesce to form a bigger drop. The terminal velocity of bigger drop is _________ \(cm / s\).

Time taken by light to travel in two different materials \(A\) and \(B\) of refractive indices \(\mu_{A}\) and \(\mu_{B}\) of same thickness is \(t_{1}\) and \(t_{2}\) respectively. If \(t_{2}-t_{1}=5 \times 10^{-10}\) s and the ratio of \(\mu_{A}\) to \(\mu_{B}\) is \(1: 2\). Then the thickness of material, in meter is: (Given \(v_{A}\) and \(v_{B}\) are velocities of light in \(A\) and \(B\) materials respectively).

A body of mass \(1 kg\) begins to move under the action of a time dependent force \(\vec{F}=\left(t \hat{i}+3 t^2 \hat{ j }\right) N\). where \(\hat{i}\) and \(\hat{j}\) are the unit vectors along \(x\) and \(y\) axis. The 10.Power developed by above force, at the time \(t=2 s\). will be \(..............W\).

Two blocks of mass \(2 \mathrm{~kg}\) and \(4 \mathrm{~kg}\) are connected by a metal wire going over a smooth pulley as shown in figure. The radius of wire is \(4.0 \times 10^{-5}\) \(\mathrm{m}\) and Young's modulus of the metal is \(2.0 \times 10^{11} \mathrm{~N} / \mathrm{m}^2\). The longitudinal strain developed in the wire is \(\frac{1}{\alpha \pi}\). The value of \(\alpha\) is _______. [Use \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\) )

An experiment is performed to determine the \(I-V\) characteristics of a Zener diode, which has a protective resistance of \(R = 100 \,\Omega ,\) and a maximum power of dissipation rating of \(1\,W\) .The minimum voltage range of the \(DC\) source in the circuit is