A nucleus disintegrates into two nuclear parts, in such a way that ratio of their nuclear sizes is \(1: 2^{1 / 3}\).Their respective speed have a ratio of \(n: 1\). The value of \(n\) is \(.....\).

\(LED\) is constructed from \(Ga-As-P\) semiconducting material. The energy gap of this \(LED\) is \(1.9\, eV\). Calculate the wavelength of light emitted and its colour. \(\left[ h =6.63 \times 10^{-34} \;Js \right.\) and \(\left. c =3 \times 10^{8}\; ms ^{-1}\right]\)

When a particle of mass \(m\) is attached to a vertical spring of spring constant \(k\) and released, its motion is described by \(y ( t )= y _{0} \sin ^{2} \omega t ,\) where \('y'\) is measured from the lower end of unstretched spring. Then \(\omega\) is

A sample contains \(10^{-2}\, kg\) each of two substances A and \(B\) with half lives \(4 \,s\) and \(8 \,s\) respectively. The ratio of then atomic weights is \(1: 2\) The ratio of the amounts of \(A\) and \(B\) after \(16 \,s\) is \(\frac{x}{100}\). the value of \(x\) is........

A rigid massless road of length \(3l\) has tow masses attached at each end as shown in the figure. The rod is pivoted at point \(P\) on the horizontal axis (see figure). When released from initial horizontal position, its instantaneous angular acceleration will be

A particle of mass \(1\, {kg}\) is hanging from a spring of force constant \(100\, {Nm}^{-1 .}\) The mass is pulled slightly downward and released so that it executes free simple harmonic motion with time period \({T}\). The time when the kinetic energy and potential energy of the system will become equal, is \(\frac{{T}}{{x}}\). The value of \({x}\) is ..... .

A fluid is flowing through a horizontal pipe of varying cross-section, with speed \(v\;ms^{-1}\) at a point where the pressure is \(P\) Pascal. At another point where pressure is \(\frac{ P }{2}\) Pascal its speed is \(V\;ms^{-1}\). If the density of the fluid is \(\rho\, kg\, m ^{-3}\) and the flow is streamline, then \(V\) is equal to

A series \(AC\) circuit containing an inductor \((20\,mH),\) a capacitor \((120\,\mu F)\) and a resistor \((60\, \Omega )\) is driven by an \(AC\) source of \(24\,V/50\,Hz.\) The energy dissipated in the circuit in \(60\,s\) is

If the time period \(t\) of the oscillation of a drop of liquid of density \(d\), radius \(r\), vibrating under surface tension \(s\) is given by the formula \(t = \sqrt {{r^{2b}}\,{s^c}\,{d^{a/2}}} \) . It is observed that the time period is directly proportional to \(\sqrt {\frac{d}{s}} \) . The value of \(b\) should therefore be

the given potentiometer has its wire of resistance \(10\, \Omega\). When the sliding contact is in the middle of the potentiometer wire, the potential drop across \(2\, \Omega\) resistor is -