In an engine the piston undergoes vertical simple harmonic motion with amplitude \(7\, cm\) . A washer rests on top of the piston and moves with it. The motor speed is slowly increased. The frequency of the piston at which the washer no longer stays in contact with the piston, is close to ...... \(Hz\)

An electron in a hydrogen atom revolves around its nucleus with a speed of \(6.76 \times 10^6\,ms ^{-1}\) in an orbit of radius \(0.52\,\mathring A\). The magnetic field produced at the nucleus of the hydrogen atom is \(......T\).

A Carnot freezer takes heat from water at \(0\,^oC\) inside it and rejects it to the room at a temperature of \(27\,^oC\). The latent heat of ice is \(336 \times 10^3\, J\,kg^{-1}\).  lf \(5\, kg\) of water at \(0\,^oC\) is converted into ice at  \(0\,^oC\) by the freezer, then the energy consumed by the freezer is close to

In the figure shown below, the charge on the left plate of the \(10\, \mu F\) capacitor is \(-30\,\mu C.\) The charge on the right place of the \(6\,\mu F\) capacitor is.....\(\mu C\)

Figure represents the extension (\(\Delta l\)) of a wire of length \(1\) meter, suspended from the ceiling of the room at one end with a load \(W\) connected to the other end. If the cross-sectional area of the wire is \(10^{-5}\) m\(^2\) then the Young's modulus of the wire is __________ N/m\(^2\).

In a Young's double slit experiment, the separation between the slits is \(0.15\; \mathrm{mm}\). In the experiment, a source of light of wavelength \(589 \;\mathrm{nm}\) is used and the interference pattern is observed on a screen kept \(1.5\; \mathrm{m}\) away. The separation between the successive bright fringes on the screen is......\(mm\)

In a Young double slit experiment, the wavelength of incident light is \(6000\) Å, the separation between slits \(S_1\) and \(S_2\) is \(5\) cm and the distance between slits plane and screen is \(50\) cm, as shown in the figure below. If the resultant intensity at \(P\) is equal to the intensity due to individual slits, the path difference between interfering waves is __________ Å.

The electric field a plane electromagnetic wave is given by :
\(E _y=69 \sin \left[0.6 \times 10^3 x -1.8 \times 10^{11} t \right] V / m\).
The expression for magnetic field associated with this electromagnetic wave is _________ T.

Match List \(− I\) (Event) with List \(−II \) (Order of the time interval for happening of the event) and select the correct option from the options given below the lists

List \(- I\)	List \(- II\)
\((1)\) Rotation period of earth	\((i)\) \(10^5\, s\)
\((2)\) Revolution period of earth	\((ii)\) \(10^7\, s\)
\((3)\) Period of light wave	\((iii)\) \(10^{-15}\, s\)
\((4)\) Period of sound wave	\((iv)\) \(10^{-3}\, s\)

The force required to stretch a wire of crosssection \(1 cm ^{2}\) to double its length will be ........ \( \times 10^{7}\,N\) (Given Yong's modulus of the wire \(=2 \times 10^{11}\,N / m ^{2}\) )