The velocity of the bullet becomes one third after it penetrates \(4\,cm\) in a wooden block. Assuming that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at \((4+x)\,cm\) inside the block. The value of \(x\) is\(.....\)

Mobility of electron in a semiconductor is defined as the ratio of their drift velocity to the applied electric field. If, for an \(n-\) type semiconductor, the density of electrons is \(10^{19}\, m^{-3}\) and their mobility is \(1.6\, m^2\,/(V.s)\) then the resistivity of the semiconductor(since it is an \(n-\) type semiconductor contribution of holes is ignored) is close to ................ \(\Omega  m\)

If the length of a wire is made double and radius is halved of its respective values. Then, the Young's modules of the material of the wire will :

The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by \(0.02 \%\) is ______ \(\mathrm{m}\). (Take density of sea water \(=10^3 \mathrm{kgm}^{-3}\), Bulk modulus of rubber \(=9 \times 10^8 \mathrm{Nm}^{-2}\), and \(\mathrm{g}=10 \mathrm{~ms}^{-2}\) )

A pendulum with time period of \(1\, s\) is losing energy due to damping. At certain time its energy is \(45\, J\). If after  completing \(15\,oscillations\) , its energy has become \(15\, J\), its damping constant (in \(s^{-1}\) ) is

\(c_P\) and \(c_V\) are specific heats at constant pressure and constant volume respectively. It is observed that \(c_P - c_V = a\) for hydrogen gas \(c_P - c_V = b\) for nitrogen gas The correct relation between \(a\) and \(b\) is

A hemispherical glass body of radius \(10\, cm\) and refractive index \(1.5\) is silvered on its curved surface. A small air bubble is \(6\, cm\) below the flat surface inside it along the axis. The position of the image of the air bubble made by the mirror is seen 

Match List \(I\) with List \(II\)

List \(I\)	List \(II\)
\((A)\) Young's Modulus \((Y)\)	\((I)\) \(\left[ M L ^{-1} T ^{-1}\right]\)
\((B)\) Co-efficient of Viscosity \((\eta)\)	\((II)\) \(\left[ M L ^2 T ^{-1}\right]\)
\((C)\) Planck's Constant \((h)\)	\((III)\) \(\left[ M L ^{-1} T ^{-2}\right]\)
\((D)\) Work Function \((\phi)\)	\((IV)\) \(\left[ M L ^2 T ^{-2}\right]\)

Choose the correct answer from the options given below:

A Zener of breakdown voltage \(V_{z}=8\,V\) and maximum zener current, \(I _{ ZM }=10\,mA\) is subjected to an input voltage \(V _{ i }=10\,V\) with series resistance \(R=100\,\Omega\). In the given circuit \(R_{L}\) represents the variable load resistance. The ratio of maximum and minimum value of \(R_{L}\) is