In a Young's double slit experiment \(15\) fringes are observed on a small portion of the screen when light of wavelength \(500 \;\mathrm{nm}\) is used. Ten fringes are observed on the same section of the screen when another light source of wavelength \(\lambda\) is used. Then the value of \(\lambda\) is (in \(\mathrm{nm})\)

A particle is moving in a straight line. The variation of position ' \(x\) ' as a function of time ' \(t\) ' is given as \(x=\left(t^3-6 t^2+20 t+15\right) m\). The velocity of the body when its acceleration becomes zero is _______.

A thin circular ring of mass \(M\) and radius \(R\) is rotating with a constant angular velocity \(2 \; rads ^{-1}\) in a horizontal plane about an axis vertical to its plane and passing through the center of the ring. If two objects each of mass \(m\) be attached gently to the opposite ends of a diameter of ring, the ring will then rotate with an angular velocity (in \(rads ^{-1}\) )

An engine approaches a hill with a constant speed. When it is at a distance of \(0.9\, km\), it blows a whistle whose echo is heard by the driver after \(5\, seconds\). If the speed of sound in air is \(330\, m/s\), then the speed of the engine is .... \(m/s\)

Interference fringes are observed on a screen by illuminating two thin slits \(1 \,mm\) apart with a light source \((\lambda=632.8\, nm )\). The distance between the screen and the slits is \(100\, cm\). If a bright fringe is observed on a screen at a distance of \(1.27\, mm\) from the central bright fringe, then the path difference between the waves, which are reaching this point from the slits is close to\(....\mu m\)

The root mean square velocity of molecules of gas is

Light is incident from a medium into air at two possible angles of incidence \((A)\, 20^o\) and \((B)\, 40^o\) . In the medium light travels \(3.0\, cm\) in \(0.2\, ns\). The ray will

The radius of gyration of a cylindrical rod about an axis of rotation perpendicular to its length and passing through the center will be \(....m\) Given, the length of the rod is \(10 \sqrt{3} m\).

Under isothermal condition, the pressure of a gas is given by \(P = aV ^{-3}\), where \(a\) is a constant and \(V\) is the volume of the gas. The bulk modulus at constant temperature is equal to \(..........\,P\)

A zener diode of power rating \(2\, {W}\) is to be used as a voltage regulator. If the zener diode has a breakdown of \(10 \,{V}\) and it has to regulate voltage fluctuated between \(6\, {V}\) and \(14\, {V}\), the value of \({R}_{{s}}\) for safe operation should be \(....\Omega\)

A large number of water drops, each of radius \(r\), combine to have a drop of radius \(R\). If the surface tension is \(T\) and mechanical equivalent of heat is \(J ,\) the rise in heat energy per unit volume will be

In a circuit for finding the resistance of a galvanometer by half deflection method, a  \(6\,V\)  battery and a high resistance of  \(11\,k\Omega \)  are used. The figure of merit of the galvanometer \(60\,\mu A/\)  division. In the absence of shunt resistance, the galvanometer produces a deflection of  \(\theta = 9\)  divisions when current flows in the circuit. The value of the shunt resistance that can cause the deflection of \(\theta /2 ,\)  is closest to ..................  \(\Omega\)