There is an air bubble of radius \(1.0\,mm\) in a liquid of surface tension \(0.075\,Nm ^{-1}\) and density \(1000\,kg\) \(m ^{-3}\) at a depth of \(10\,cm\) below the free surface. The amount by which the pressure inside the bubble is greater than the atmospheric pressure is \(....Pa \left( g =10\,ms ^{-2}\right)\)

The magnetic field associated with a light wave is given, at the origin, by \(B = B_0 [sin\,(3.14 \times 10^7)\,ct\,+\,sin\,(6.28 \times 10^7)\,ct]\) If this light falls on a silver plate having a work function of \(4.7\,eV,\) what will be the maximum kinetic energy of the photo electrons? .............. \(eV\)

A uniform rod \(A B\) of mass \(2 \mathrm{~kg}\) and Length \(30 \mathrm{~cm}\) at rest on a smooth horizontal surface. An impulse of force \(0.2\  \mathrm{Ns}\) is applied to end \(B.\) The time taken by the rod to turn through at right angles will be \(\frac{\pi}{\mathrm{x}}\ \mathrm{s}\), where  X = _______.

In a screw gauge the zero of main scale reference line coincides with the fifth division of the circular scale when two studs are in contact. There are \(100\) divisions in circular scale and pitch of screw gauge is \(0.1\) mm. When diameter of a sphere is measured, the reading of main scale is \(5\) mm and \(50^{\text{th}}\) division of circular scale coincides with the reference line of main scale. The diameter of sphere is _______ mm.

The diameter of the objective lens of microscope makes an angle \(\beta \) at the focus of the microscope. Further, the medium between the object and the lens is an oil of refractive index \(n\). Then the resolving power of the microscope

Find the correct combination of A, B, C and D inputs which can cause the LED to glow

A liquid of density \(750\,kgm ^{-3}\) flows smoothly through a horizontal pipe that tapers in crosssectional area from \(A _{1}=1.2 \times 10^{-2}\,m ^{2}\) to \(A_{2}=\frac{A_{1}}{2}\). The pressure difference between the wide and narrow sections of the pipe is \(4500\,Pa\). The rate of flow of liquid is________\(\times 10^{-3}\,m ^{3} s ^{-1}\)

A circular disc of mass \(M\) and radius \(R\) is rotating about its axis with angular speed \(\omega_{1}\) If another stationary disc having radius \(\frac{ R }{2}\) and same mass \(M\) is dropped co-axially on to the rotating disc. Gradually both discs attain constant angular speed \(\omega_{2}\). The energy lost in the process is \(p \%\) of the initial energy. Value of \(p\) is

Two cars \(P\) and \(Q\) are moving on a road in the same direction. Acceleration of car \(P\) increases linearly with time whereas car \(Q\) moves with a constant acceleration. Both cars cross each other at time \(t=0\), for the first time. The maximum possible number of crossing(s) (including the crossing at \(t=0)\) is ________.

A source supplies heat to a system at the rate of \(1000 \,W\). If the system performs work at a rate of \(200\,W\). The rate at which internal energy of the system increases \(.......\,W\)

A monochromatic light is incident on a hydrogen sample in ground state. Hydrogen atoms absorb a fraction of light and subsequently emit radiation of six different wavelengths. The frequency of incident light is \(x \times 10^{15}\,Hz\). The value of \(x\) is (Given \(h =4.25 \times 10^{-15}\,eVs\) )

A potentiometer wire \(PQ\) of \(1\,m\) length is connected to a standard cell \(E _{1}\). Another cell \(E _{2}\) of emf \(1.02\, V\) is connected with a resistance \('r'\) and switch \(S\) (as shown in figure). With switch \(S\) open, the null position is obtained at a distance of \(49\, cm\) from \(Q\). The potential gradient in the potentiometer wire is.......\(V/cm\)

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason \(\mathrm{R}\) Assertion A : Work done in moving a test charge between two points inside a uniformly charged spherical shell is zero, no matter which path is chosen.
Reason \(\mathrm{R}\) : Electrostatic potential inside a uniformly charged spherical shell is constant and is same as that on the surface of the shell. In the light of the above statements, choose the correct answer from the options given below