In meter bridge experiment for measuring unknown resistance ' \(S\) ', the null point is obtained at a distance \(30 cm\) from the left side as shown at point \(D\). If \(R\) is \(5.6 k \Omega\), then the value of unknown resistance ' \(S\) ' will be \(\Omega .\)

A proton and an electron are associated with same de-Broglie wavelength. The ratio of their kinetic energies is _______. (Assume \(\mathrm{h}=6.63 \times 10^{-34} \mathrm{~J} \mathrm{~s}, \mathrm{~m}_{\mathrm{e}}=9.0 \times 10^{-31} \mathrm{~kg}\) and \(\mathrm{m}_{\mathrm{p}}=1836\) times \(\mathrm{m}_{\mathrm{e}}\) )

Statement\(-I :\) To get a steady de output from the pulsating voltage received from a full wave rectifier we can connect a capacitor across the output parallel to the load \({R}_{{L}}\) Statement\(-II :\) To get a steady de output from the pulsating voltage received from a full wave rectifier we can connect an inductor in series with \({R}_{{L}}\). In the light of the above statements, choose the most appropriate answer from the options given below:

A juggler throws balls vertically upwards with same initial velocity in air. When the first ball reaches its highest position, he throws the next ball. Assuming the juggler throws \(n\) balls per second, the maximum height the balls can reach is

Two springs of force constants \(300\, N/m\) (Spring \(A\)) and \(400\, N/m\) (Spring \(B\)) are joined together in series . The combination is compressed by \(8.75\, cm\). The ratio of energy stored in \(A\) and \(B\) is  \(\frac{{{E_A}}}{{{E_B}}}\).  Then \(\frac{{{E_A}}}{{{E_B}}}\) is equal to

A light unstretchable string passing over a smooth light pulley connects two blocks of masses \(m_1\) and \(m_2\). If the acceleration of the system is \(\frac{g}{8}\), then the ratio of the masses \(\frac{\mathrm{m}_2}{\mathrm{~m}_1}\) is _______.

The moment of inertia of a uniform cylinder of length \(l\) and radius \(R\) about its perpendicular bisector is \(I\). What is the ratio \(l/R\) such that the moment of inertia is minimum?

A block of mass \(1.9\, kg\) is at rest at the edge of a table, of height \(1\, m\). A bullet of mass \(0.1\, kg\) collides with the block and sticks to it. If the velocity of the bullet is \(20\, m / s\) in the horizontal direction just before the collision then the kinetic energy just before the combined system strikes the floor, is \(....J\) [Take \(g =10\, m / s ^{2}\). Assume there is no rotational motion and loss of energy after the collision is negligable. \(]\)

A solid steel ball of diameter 3.6 mm acquired terminal velocity \(2.45 \times 10^{-2} \mathrm{~m} / \mathrm{s}\) while falling under gravity through an oil of density \(925 \mathrm{~kg} \mathrm{~m}^{-3}\). Take density of steel as \(7825 \mathrm{~kg} \mathrm{~m}^{-3}\) and g as 9.8 \(\mathrm{m} / \mathrm{s}^2\). The viscosity of the oil in SI unit is

Water flows in a horizontal pipe whose one end is closed with a valve. The reading of the pressure gauge attached to the pipe is \(P_1\). The reading of the pressure gauge falls to \(P_2\) when the valve is opened. The speed of water flowing in the pipe is proportional to

Two point charges \(-4 \mu c\) and \(4 \mu c\), constituting an electric dipole, are placed at \((-9,0,0) \mathrm{cm}\) and \((9,0,0) \mathrm{cm}\) in a uniform electric field of strength \(10^4 \mathrm{NC}^{-1}\). The work done on the dipole in rotating it from the equilibrium through \(180^{\circ}\) is :

A spring stretches by \(2\) mm when it is loaded with a mass of \(200\) g. From equilibrium position the mass is further pulled down by \(2\) mm and released. The frequency associated with the system and maximum energy in the spring are __________ Hz and __________ J, respectively. (Take g \(= 10\) m/s\(^2\))