A wooden block of mass \(5 \mathrm{~kg}\) rests on soft horizontal floor. When an iron cylinder of mass \(25\) \(\mathrm{kg}\) is placed on the top of the block, the floor yields and the block and the cylinder together go down with an acceleration of \(0.1 \mathrm{~ms}^{-2}\). The action force of the system on the floor is equal to _______.

In Young's double slit experiment the two slits are \(0.6 \; mm\) distance apart. Interference pattern is observed on a screen at a distance \(80 \; cm\) from the slits. The first dark fringe is observed on the screen directly opposite to one of the slits. The wavelength of light will be \(\dots \; nm .\)

Which of the following circuits represents a forward biased diode?


Choose the correct answer from the options given below :

An aeroplane, with its wings spread \(10\, m ,\) is flying at a speed of \(180 \,km / h\) in a horizontal direction. The total intensity of earth's field at that part is \(2.5 \times 10^{-4}\, Wb / m ^{2}\) and the angle of dip is \(60^{\circ}\). The emf induced between the tips of the plane wings will be ...... \(mV\)

\(M\) grams of steam at \(100^{\circ} \mathrm{C}\) is mixed with \(200\; \mathrm{g}\) of ice at its melting point in a thermally insulated container. If it produces liquid water at \(40^{\circ} \mathrm{C}\) [heat of vaporization of water is \(540 \;cal/\mathrm{g}\) and heat of fusion of ice is \(80 \;\text { cal/g }]\) the value of \(\mathrm{M}\) is

A body \(A,\) of mass \(m=0.1\; kg\) has an initial velocity of \(3 \hat{\mathrm{i}}\; \mathrm{ms}^{-1} .\) It collides elastically with another body, \(\mathrm{B}\) of the same mass which has an initial velocity of \(5 \hat{\mathrm{j}} \;\mathrm{ms}^{-1}\). After collision. A moves with a velocity \(\overline{\mathrm{v}}=4(\hat{\mathrm{i}}+\hat{\mathrm{j}})\). The energy of \(\mathrm{B}\) after collision is written as \(\frac{\mathrm{x}}{10} \;\mathrm{J}\) The value of \(x\) is

A gas molecule of mass \(M\) at the surface of the Earth has kinetic energy equivalent to \(0\,^oC\). If it were to go up straight without colliding with any other molecules, how high it would rise? Assume that the height attained is much less than radius of the earth. (\(k_B\) is Boltzmann constant)

The root mean square speed of molecules of nitrogen gas at \(27^{\circ} C\) is approximately\(.......m/s\)(Given mass of a nitrogen molecule \(=4.6 \times 10^{-26}\,kg\) and take Boltzmann constant  \(k _{ B }=1.4 \times 10^{-23}\,JK ^{-1}\) )

Two short bar magnets oflength \(1\ cm\) each have magnetic moments \(1.20\ Am^2\) and \(1.00\ Am^2\) respectively. They are placed on a horizontal table parallel to each other with their \(N\) poles pointing towards the South. They have a common magnetic equator and are separated by a distance of \(20.0\ cm\). The value of the resultand horizontal magnetic induction at the mid-point \(O\) of the line joining their centres is close to  (Horizontal component of earth.s magnetic induction is \(3.6 \times  10^{-5}\) \(Wbm^{-2}\)  )

Two coherent monochromatic light beams of intensities \(I\) and \(4I\) are superimposed. The difference between maximum and minimum possible intensities in the resulting beam is \(x\)I. The value of \(x\) is _______.