A horizontal straight wire \(5 \mathrm{~m}\) long extending from east to west falling freely at right angle to horizontal component of earth's magnetic field \(0.60 \times 10^{-4} \ \mathrm{Wbm}^{-2}\). The instantaneous value of emf induced in the wire when its velocity is \(10 \mathrm{~ms}^{-1}\) is _______ \(\times 10^{-3} \mathrm{~V}\)

A light of energy \(12.75 \;eV\) is incident on a hydrogen atom in its ground state. The atom absorbs the radiation and reaches to one of its excited states. The angular momentum of the atom in the excited state is \(\frac{x}{\pi} \times 10^{-17} \;eVs\). The value of \(x\) is \(........\) (use \(h=4.14 \times 10^{-15} \;eVs , c=3 \times 10^8\;\left.ms ^{-1}\right)\)

Two satellites \(A\) and \(B\) having masses in the ratio \(4: 3\) are revolving in circular orbits of radii \(3\,r\) and \(4\,r\) respectively around the earth. The ratio of total mechanical energy of \(A\) to \(B\) is.

The exit surface of a prism with refractive index \(n\) is coated with a material having refractive index \(\frac{ n }{2}\). When this prism is set for minimum angle of deviation it exactly meets the condition of critical angle. The prism angle is _________

A stone of mass \(900 \mathrm{~g}\) is tied to a string and moved in a vertical circle of radius \(1 \mathrm{~m}\) making \(10\  \mathrm{rpm}\). The tension in the string, when the stone is at the lowest point is _______. (if \(\pi^2=9.8\) and \(g=9.8 \mathrm{~m} / \mathrm{s}^2\) )

Refer to the figure given below, current between terminals \(A\) and \(B\) is _____ A.

A string is clamed at both the ends and it is vibrating in its \(4^{th}\) harmonic. The equation of the stationary wave is \(Y =0.3\,sin\,(0.157\,x) \,cos\,(200\pi t)\). The length of the string is ..... \(m\) (all quantities are in \(SI\) units)

Match List \(I\) with List \(II\)

List - \(I\)	List - \(II\)
\((A)\) Torque	\((I)\) \({\left[\mathrm{M}^1 \mathrm{~L}^1 \mathrm{~T}^{-2} \mathrm{~A}^{-2}\right]}\)
\((B)\) Magnetic fileld	\((II)\) \(\left[\mathrm{L}^2 \mathrm{~A}^1\right]\)
\((C)\) Magneti moment	\((III)\) \({\left[\mathrm{M}^1 \mathrm{~T}^{-2} \mathrm{~A}^{-1}\right]}\)
\((D)\) permeability of free space	\((IV)\) \(\left[\mathrm{M}^1 \mathrm{~L}^2 \mathrm{~T}^{-2}\right]\)

Choose the correct answer from the options given below :

Given below are two statements: \(Statement\) \(I\) : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in hot water. \(Statement\) \(II\) : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in cold water. In the light of the above statements, choose the most appropriate from the options given below