The velocity of a small ball of mass \(0.3\,g\) and density \(8\,g / cc\) when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is \(1.3\,g / cc\), then the value of viscous force acting on the ball will be \(x \times 10^{-4}\,N\), the value of \(x\) is [use \(g=10\,m / s ^{2}\) ] 

Match List\(-I\) with List\(-II\).

List\(-I\)	List\(-II\)
\(A\). Gauss's Law in Electrostatics	\(I\). \(\oint \vec{E} \cdot d \vec{l}=-\frac{d \phi_B}{d t}\)
\(B\). Faraday's Law	\(II\). \(\oint \overrightarrow{ B } \cdot d \overrightarrow{ A }=0\)
\(C\). Gauss's Law in Magnetism	\(III\). \(\oint \vec{B} \cdot d \vec{l}=\mu_0 i_C+\mu_0 \in_0 \frac{d \phi_E}{d t}\)
\(D\). Ampere-Maxwell Law	\(IV\). \(\oint \overrightarrow{ E } \cdot d \overrightarrow{ s }=\frac{ q }{\epsilon_0}\)

Choose the correct answer from the options given below:

For an experimental expression \(y=\frac{32.3 \times 1125}{27.4}\), where all the digits are significant. Then to report the value of \(y\) we should write

In a meter bridge experiment the balance point in obtained if the gaps are closed by \(2\,\Omega\) and \(3\,\Omega\). A shunt of \(x\,\Omega\) is added to \(3\,\Omega\) resistor to shift the balancing point by \(22.5\,cm\). The value of \(X\) is \(................\)

A container is divided into two chambers by a partition. The volume of first chamber is \(4.5\) litre and second chamber is \(5.5\) litre. The first chamber contain \(3.0\) moles of gas at pressure \(2.0\, atm\) and second chamber contain \(4.0\) moles of gas at pressure \(3.0\, atm\) .After the partition is removed and the mixture attains equilibrium, then, the common equilibrium pressure existing in the mixture is \(x \times 10^{-1} atm\). Value of \(x\) is.........

Consider following statements:
A. Surface tension arises due to extra energy of the molecules at the interior as compared to the molecules at the surface, of a liquid.
B. As the temperature of liquid rises, the coefficient of viscosity increases.
C. As the temperature of gas increases, the coefficient of viscosity increases
D. The onset of turbulence is determined by Reynold's number.
E. In a steady flow two stream lines never intersect.
Choose the correct answer from the options given below:

The metallic bob of simple pendulum has the relative density \(5\). The time period of this pendulum is \(10\,s\). If the metallic bob is immersed in water, then the new time period becomes \(5 \sqrt{ x } s\). The value of \(x\) will be.

A \(10\,\mu C\) charge is divided into two parts and placed at \(1\,cm\) distance so that the repulsive force between them is maximum. The charges of the two parts are :

Magnetic flux (in weber) in a closed circuit of resistance \(20\,\Omega\) varies with time \(t(s)\) as \(\phi=8 t ^{2}-9 t +5\). The magnitude of the induced current at \(t =0.25\,s\) will be \(...mA\)

The root mean square velocity of molecules of gas is