A \(20\, Henry\) inductor coil is connected to a \(10\, ohm\) resistance in series as shown in figure. The time at which rate of dissipation of energy (Joule’s heat) across resistance is equal to the rate at which magnetic energy is stored in the inductor, is

A physical quantity C is related to four other quantities \(\mathrm{p}, \mathrm{q}, \mathrm{r}\) and s as follows \(\mathrm{C}=\frac{\mathrm{pq}^2}{\mathrm{r}^3 \sqrt{\mathrm{~s}}}\)
The percentage errors in the measurement of \(\mathrm{p}, \mathrm{q}, \mathrm{r}\) and s are \(1 \%, 2 \% 3 \%\) and \(2 \%\) respectively. The percentage error in the measurement of C will be _____\(\%\).

Given are statements for certain thermodynamic variables,
(A) Internal energy, volume (V) and mass (M) are extensive variables.
(B) Pressure (P), temperature (T) and density ( \(\rho\) ) are intensive variables.
(C) Volume (V), temperature (T) and density ( \(\rho\) ) are intensive variables.
(D) Mass (M), temperature (T) and internal energy are extensive variables.

Choose the correct answer from the options given below :

A sand dropper drops sand of mass \(m(t)\) on a conveyer belt at a rate proportional to the square root of speed \((v)\) of the belt, i.e. \(\frac{\mathrm{dm}}{\mathrm{dt}} \propto \sqrt{v}\). If P is the power delivered to run the belt at constant speed then which of the following relationship is true?

A block of mass \(m\), lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring constant \(k\). The other end of the spring is fixed, as shown in the figure. The block is initially at rest in a equilibrium position. If now the block is pulled with a constant force \(F\), the maximum speed of the block is

Two forces \(P\) and \(Q\), of magnitude \(2F\) and \(3F\), respectively, are at an angle \(\theta \) with each other. If the force \(Q\) is doubled, then their resultant also gets doubled. Then, the angle \(\theta \) is ....... \(^o\)

A particle is doing simple harmonic motion of amplitude \(0.06 \mathrm{~m}\) and time period \(3.14 \mathrm{~s}\). The maximum velocity of the particle is _______ \(\mathrm{cm} / \mathrm{s}\).

A long cylindrical volume contains a uniformly distributed charge of density \(\rho \;Cm ^{-3}\). The electric field inside the cylindrical volume at a distance \(x =\frac{2 \varepsilon_{0}}{\rho} m\) from its axis is \(.......Vm ^{-1}\)

A quantity Q is formulated as \(\mathrm{X}^{-2} \mathrm{Y}^{+\frac{3}{2}} \mathrm{Z}^{-\frac{2}{5}} \cdot \mathrm{X}, \mathrm{Y}\) and Z are independent parameters which have fractional errors of \(0.1,0.2\) and 0.5 , respectively in measurement. The maximum fractional error of Q is _______.

Two identical cells each of emf \(1.5\,V\) are connected in series across a \(10\,\Omega\) resistance. An ideal voltmeter connected across \(10\,\Omega\) resistance reads \(1.5\,V\). The internal resistance of each cell is \(......\Omega\).