A bullet of mass \(20\,g\) has an initial speed of \(1\,ms^{-1}\) just before it starts penetrating a mud wall of thickness \(20\,cm.\) If the wall offers a mean resistances of \(2.5 \times 10^{-2}\,N,\) the speed of the bullet after emerging from the other side of the wall is close to .............. \(\mathrm{ms}^{-1}\)

Choose the correct nuclear process from the below options.
[p: proton, n : neutron, \(\mathrm{e}^{-}\): electron, \(\mathrm{e}^{+}\): positron, \(v:\) neutrino, \(\bar{v}\) : antineutrino]

If electronic charge \(e\), electron mass \(m\), speed of light in vacuum \(c\) and Planck 's constant \(h\) are taken as fundamental quantities, the permeability of vacuum \(\mu _0\) can be expressed in units of

Particle \(A\) of mass \(m _{1}\) moving with velocity \((\sqrt{3} \hat{i}+\hat{j})\, ms ^{-1}\) collides with another particle \(B\) of mass \(m _{2}\) which is at rest initially. Let \(\overrightarrow{ V }_{1}\) and \(\overrightarrow{ V }_{2}\) be the velocities of particles \(A\) and \(B\) after collision respectively. If \(m _{1}=2\, m _{2}\) and after collision \(\overrightarrow{ V }_{1}=(\hat{ i }+\sqrt{3} \hat{ j })\, ms ^{-1},\) the angle between \(\overrightarrow{ V }_{1}\) and \(\overrightarrow{ V }_{2}\) is\(......^o\)

A negative test charge is moving near a long straight wire carrying a current. The force acting on the test charge is parallel to the direction of the current. The motion of the charge is

A magnet hung at \(45^{\circ}\) with magnetic meridian makes an angle of \(60^{\circ}\) with the horizontal. The actual value of the angle of dip is.

A liquid of density \(\rho \) is coming out of a hose pipe of radius \(a\) with horizontal speed \(v\) and hits a mesh. \(50\%\) of the liquid passes through the mesh unaffected. \(25\%\) looses all of its momentum and \(25\%\) comes back with the same speed. The resultant pressure on the mesh will be

A charge of \(4.0 \mu \mathrm{C}\) is moving with a velocity of \(4.0 \times 10^6 \mathrm{~ms}^{-1}\) along the positive \(\mathrm{y}\)-axis under a magnetic field \(\vec{B}\) of strength \((2 \hat{k})\  T\). The force acting on the charge is \(x \hat{i} N\). The value of \(x\) is _______.

Two radioactive substances A and B of mass numbers \(200\) and \(212\) respectively, shows spontaneous \(\alpha\)-decay with same \(Q\) value of \(1\) MeV. The ratio of energies of \(\alpha\)-rays produced by A and B is ________.

In a physical balance working on the principle of moments, when \(5\, mg\) weight is placed on the left pan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct?

This question has Statement \(- 1\) and Statement \(-2\). Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement \(1\) : The internal energy of a perfect gas is entirely kinetic and depends only on absolute temperature of the gas and not on its pressure or volume.
Statement \(2\) : A perfect gas is heated keeping pressure constant and later at constant volume. For the same amount of heat the temperature of the gas at constant pressure is lower than that at constant volume.

The work function of a substance is \(3.0\ \mathrm{eV}\). The longest wavelength of light that can cause the emission of photoelectrons from this substance is approximately _______.

A body of mass \(m= 10^{-2}\) \(kg\) is moving in a medium and experiences a frictional force \(F= -kv^2\). Its initial speed is \(v_0= 10\) \(ms^{-1}\). If, after \(10\; s\), its energy is \(\frac{1}{8}\) \(mv_0^2\) the value of \(k\) will be