Nitrogen gas is at \(300^{\circ} C\) temperature. The temperature (in \(K\)) at which the \(rms\) speed of a \(H _{2}\), molecule would be equal to the \(rms\) speed of a nitrogen molecule, is........ (Molar mass of \(N _{2}\) gas \(28\, g\) )

Three masses \(m_1 = 4\) kg, \(m_2 = 4\) kg and \(m_3 = 6\) kg are suspended from a fixed smooth frictionless pulley as shown in the figure below. The value of \(T_1/T_2\) is _____.
(take \(g = 10\) m/s\(^2\))

A charge \(q\) is placed at the center of one of the surface of a cube. The flux linked with the cube is _______.

A particle which is experiencing a force, given by \(\vec F = 3\vec i -12\vec j\), undergoes a displacement of \(\vec d = 4\vec i\) . If the particle had a kinetic energy of \(3\, J\) at the beginning of the displacement, what is its kinetic energy at the end of the displacement?

In Young's double slit experiment, carried out with light of wavelength \(5000\) \(A\), the distance between the slits is \(0.3 \mathrm{~mm}\) and the screen is at \(200 \mathrm{~cm}\) from the slits. The central maximum is at \(x=0 \mathrm{~cm}\). The value of \(\mathrm{x}\) for third maxima is _______ \(\mathrm{mm}\).

A letter \('A'\) is constructed of a uniform wire with resistance \(1.0\,\Omega \) per \(cm\) , The sides of the letter are \(20\, cm\) and the cross piece in the middle is \(10\, cm\) long. The apex angle is \(60\) . The resistance between the ends of the legs is close to ................ \(\Omega\)

A sonometer wire of resonating length \(90 \mathrm{~cm}\) has a fundamental frequency of \(400 \mathrm{~Hz}\) when kept under some tension. The resonating length of the wire with fundamental frequency of \(600 \mathrm{~Hz}\) under same tension ________ \(\mathrm{cm}\).

With what speed should a galaxy move outward with respect to earth so that the sodium-D line at wavelength \(5890\) \(\stackrel{\circ}{{A}}\) is observed at \(5896\) \(\stackrel{\circ}{{A}}\) ? (in \({km} / {sec}\))

A moving coil galvanometer has a coil with \(175\, turns\) and area \(1\, cm^2\) It uses a torsion band of torsion constant \(10^{-6}\, N\, -m/rad\). The coil is placed in a magnetic field \(B\) parallel to its plane. The coil deflects by \(10\) for a current of \(1\, mA\). The value of \(B\) (in Tesla) is approximately

An \(AC\) source rated \(220\, V , 50\, Hz\) is connected to a resistor. The time taken by the current to change from its maximum to the rms value is

In a test experiment on a model aeroplane in wind tunnel, the flow speeds on the upper and lower surfaces of the wings are \(70 \mathrm{~ms}^{-1}\) and \(65 \mathrm{~ms}^{-1}\) respectively. If the wing area is \(2 \mathrm{~m}^2\) the lift of the wing is _______ \(\mathrm{N}\). (Given density of air \(=1.2 \mathrm{~kg} \mathrm{~m}^{-3}\) )

The graph between two temperature scales \(P\) and \(Q\) is shown in the figure. Between upper fixed point and lower fixed point there are \(150\) equal divisions of scale \(P\) and \(100\) divisions on scale \(Q\). The relationship for conversion between the two scales is given by :

A spring stretches by \(2\) mm when it is loaded with a mass of \(200\) g. From equilibrium position the mass is further pulled down by \(2\) mm and released. The frequency associated with the system and maximum energy in the spring are __________ Hz and __________ J, respectively. (Take g \(= 10\) m/s\(^2\))