The temperature of a gas is \(-78^{\circ} \mathrm{C}\) and the average translational kinetic energy of its molecules is \(\mathrm{K}\). The temperature at which the average translational kinetic energy of the molecules of the same gas becomes \(2 \mathrm{~K}\) is _______.

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Time period of a simple pendulum is longer at the top of a mountain than that at the base of the mountain.
Reason (R): Time period of a simple pendulum decreases with increasing value of acceleration due to gravity and vice-versa.
In the light of the above statements, choose the most appropriate answer from the options given below :

For the plane electromagnetic wave given by \(\mathrm{E}=\mathrm{E}_0 \sin (\omega \mathrm{t}-\mathrm{kx})\) and \(\mathrm{B}=\mathrm{B}_0 \sin (\omega \mathrm{t}-\mathrm{kx})\), the ratio of average electric energy density to average magnetic energy density is

Using a variable-frequency a.c. voltage source, the maximum current measured in the given LCR circuit is 50 mA for \(V =5 \sin (100 t )\). The values of L and \(R\) are shown in the figure. The capacitance of the capacitor \(( C )\) used is ___________ \(\mu F\).

A part of a complete circuit is shown in the figure. At some instant, the value of current \(I\) is \(1\, A\) and it is decreasing at a rate of \(10^{2}\, A s ^{-1}\) The value of the potential difference \(V _{ P }- V _{ Q }\) (in volts) at that instant, is.

The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is \(20 \,cm\). The length of the open organ pipe is........\(cm\).

A cubical block of side \(30\,cm\)  is moving with  velocity \(2\,\,ms^{-1}\) on a smooth horizontal surface. The surface has a bump at a point \(O\) as shown in figure. The angular velocity (in rad/s) of the block immediately after it hits the bump, is

A point charge causes an electric flux of \(-2 \times 10^4 \mathrm{Nm}^2 \mathrm{C}^{-1}\) to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is :
(Given \(\epsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}\) )

If \({V}_{{A}}\) and \({V}_{{B}}\) are the input voltages (either \(5\, {V}\) or \(0\, {V}\) ) and \({V}_{0}\) is the output voltage then the two gates represented in the following circuit \((A)\) and \((B)\) are:- \((A)\quad\quad\quad\quad(B)\)

If the radius of curvature of the path of two particles of same mass are in the ratio \(3:4,\) then in order to have constant centripetal force, their velocities will be in the ratio of: