The maximum potential energy of a block executing simple harmonic motion is \(25\,J\). A is amplitude of oscillation. At \(A / 2\), the kinetic energy of the block is \(...............\)

Match the LIST-I with LIST-II

List-I	List-II
A. Planck's constant	I. \(ML^2T^{-2}\)
B. Stopping potential	II. \(T^{-1}\)
C. Work function	III. \(ML^2T^{-1}\)
D. Threshold frequency	IV. \(ML^2T^{-3}A^{-1}\)

Choose the correct answer from the options given below:

A copper wire is stretched to make it \(0.5\%\) longer. The percentage change in its electric resistance if its volume remains unchanged is ................ \(\%\)

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 transverse wave is represented by  \(y = \frac{{10}}{\pi }\,\sin \,\left( {\frac{{2\pi }}{T}t - \frac{{2\pi }}{\lambda }x} \right)\) For what value of the wavelength the wave velocity is twice the maximum particle velocity ..... \(cm\) ?

The radiation corresponding to \(3 \rightarrow 2\) transition ofhydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field of \(3 \times  10^{-4}\) \(T\) If the radius of the largest circular path followed by these electrons is \(10.0\ mm\), the work function of the metal is close to......\( eV\)

Consider two satellites \(S_{1}\) and \(S_{2}\) with periods of revolution \(1\, hr\). and \(8\, hr\). respectively revolving around a planet in circular orbits. The ratio of angular velocity of satellite \(S_{1}\) to the angular velocity of satellites \(S _{2}\) is

Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is \(11.2 \mathrm{~km} / \mathrm{s}\), the escape velocity in \(\mathrm{km} / \mathrm{s}\) from the planet will be :

The space between the plates of a parallel plate capacitor is filled with a 'dielectric' whose 'dielectric constant' varies with distance as per the relation: \(K(x) = K_0 + \lambda x\) ( \(\lambda  =\) constant) The capacitance \(C,\) of the capacitor, would be related to its vacuum capacitance \(C_0\) for the relation

The two wires \(A\) and \(B\) of equal cross-section but of different materials are joined together. The ratio of Young's modulus of wire \(A\) and wire \(B\) is \(20/11\). When the joined wire is kept under certain tension the elongations in the wires \(A\) and \(B\) are equal. If the length of wire \(A\) is \(2.2\) m, then the length of wire \(B\) is _______ m.

A radioactive nucleus decays by two different process. The half life of the first process is \(5\) minutes and that of the second process is \(30\,s\). The effective half-life of the nucleus is calculated to be \(\frac{\alpha}{11}\,s\). The value of \(\alpha\) is \(..............\)

Three containers \(\mathrm{C}_{1}, \mathrm{C}_{2}\) and \(\mathrm{C}_{3}\) have water at different temperatures. The table below shows the final temperature \(T\) when different amounts of water (given in litres) are taken from each containers and mixed (assume no loss of heat during the process) \(\begin{array}{|c|c|c|c|}\hline \mathrm{C_{1 }} & {\mathrm{C}_{2}} & {\mathrm{C}_{3}} & {\mathrm{T}} \\ \hline {1 l} & {2 l} & {-} & {60^{\circ} \mathrm{C}} \\ \hline {-} & {1 l} & {2 l} & {30^{\circ} \mathrm{C}} \\ \hline  {2 l} & {-} & {1 l} & {60^{\circ} \mathrm{C}} \\ \hline  {1 l} & {1 l} & {1 l} & {\theta} \\ \hline\end{array}\) The value of \(\theta\) (in \(^{\circ} \mathrm{C}\) to the nearest integer) is