The equations of two waves are given by \(y_{1}=5 \sin 2 \pi(x-v t) \,c m\,\) \(y_{2}=3 \sin 2 \pi(x-v t+1.5) \,c m\) These waves are simultaneously passing through a string. The amplitude of the resulting wave is.........\(cm\)

The mass of proton, neutron and helium nucleus are respectively \(1.0073\,u , 1.0087\,u\) and \(4.0015\,u\). The binding energy of helium nucleus is \(.........\,MeV\)

A charge of \(4.0 \mu \mathrm{C}\) is moving with a velocity of \(4.0 \times 10^6 \mathrm{~ms}^{-1}\) along the positive \(\mathrm{y}\)-axis under a magnetic field \(\vec{B}\) of strength \((2 \hat{k})\  T\). The force acting on the charge is \(x \hat{i} N\). The value of \(x\) is _______.

Two identical spherical balls of mass \(M\) and radius \(R\) each are stuck on two ends of a rod of length \(2R\) and mass \(M\) (see figure). The moment of inertia of the system about the axis passing perpendicularly through the centre of the rod is

A transverse wave is represented by \(y=2 \sin\) \((\omega t - kx ) cm\). The value of wavelength (in \(cm\) ) for which the wave velocity becomes equal to the maximum particle velocity, will be.

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 \(.....\).

A Carnot engine with efficiency \(50\,\%\) takes heat from a source at \(600\,K\). In order to increase the efficiency to \(70\,\%\), keeping the temperature of sink same, the new temperature of the source will be \(.........\,K\)

The magnetic moment of a bar magnet is \(0.5 \mathrm{Am}^2\). It is suspended in a uniform magnetic field of \(8 \times 10^{-2} \mathrm{~T}\). The work done in rotating it from its most stable to most unstable position is _______.

A common transistor radio set requires \(12\,V (D.C.)\) for its operation. The \(D.C.\) source is constructed by using a transformer and a rectifier circuit, which are operated at \(220\, V\) \((A.C.)\) on standard domestic \(A.C.\) supply. The number of turns of secondary coil are \(24,\) then the number of turns of primary are

Water from a tap emerges vertically downwards with an initial speed of \(1.0\,ms^{-1}.\) The cross-sectional area of the tap is \(10^{-4}\,m^2.\) Assume that the pressure is constant throughout the stream of water and that flow is streamlined. The cross-sectional area of the stream, \(0.15\,m\) below the tap would be: (take \(g = 10\,ms^{-2}\) )