A monoatomic gas of mass \(4.0\, u\) is kept in an insulated container. Container is moving with velocity \(30 \,m / s\). If container is suddenly stopped then change in temperature of the gas \(\left( R =\right.\) gas constant) is \(\frac{ x }{3 R } .\) Value of \(x\) is ..........

The position vector of the centre of mass \(\vec r\, cm\) of an asymmetric uniform bar of negligible area of cross-section as shown in figure is

A 1 m long metal rod AB completes the circuit as shown in figure. The area of circuit is perpendicular to the magnetic field of 0.10 T . If the resistance of the total circuit is \(2 \Omega\) then the force needed to move the rod towards right with constant speed (v) of \(1.5 m / s\) is _________ N.

A single turn current loop in the shape of a right angle triangle with sides \(5\,cm , 12\,cm , 13\,cm\) is carrying a current of \(2\,A\). The loop is in a uniform magnetic field of magnitude \(0.75\,T\) whose direction is parallel to the current in the \(13\,cm\) side of the loop. The magnitude of the magnetic force on the \(5\,cm\) side will be \(\frac{ x }{130}\,N\). The value of \(x\) is \(..........\)

Light is incident on a metallic plate having work function \( 110\times10^{-20} \) J. If the produced photoelectrons have zero kinetic energy then the angular frequency of the incident light is __________ rad/s. (\( h=6.63\times10^{-34} \) J.s)

The displacement of a particle, executing simple harmonic motion with time period \(T\), is expressed as \(x(t)= A \sin \omega t\), where \(A\) is the amplitude. The maximum value of potential energy of this oscillator is found at \(t=T / 2 \beta\). The value of \(\beta\) is ___________.

The electric field a plane electromagnetic wave is given by :
\(E _y=69 \sin \left[0.6 \times 10^3 x -1.8 \times 10^{11} t \right] V / m\).
The expression for magnetic field associated with this electromagnetic wave is _________ T.

A potential divider circuit is shown in figure. The output voltage \(V_0\) is _______.

The first member of the Balmer series of hydrogen atom has a wavelength of \(6561\; \mathring A\). The wavelength of the second member of the Balmer series (in \(nm\)) is