\(64\) identical drops each charged upto potential of \(10\,mV\) are combined to form a bigger dorp. The potential of the bigger drop will be \(..........\,mV\)

The amplitude and phase of a wave that is formed by the superposition of two harmonic travelling waves, \(\mathrm{y}_1(\mathrm{x}, \mathrm{t})=4 \sin (\mathrm{kx}-\omega \mathrm{t})\) and \(\mathrm{y}_2(\mathrm{x}, \mathrm{t})=2 \sin \left(\mathrm{kx}-\omega \mathrm{t}+\frac{2 \pi}{3}\right)\), are \(:\)
(Take the angular frequency of initial waves same as \(\omega\))

An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity \(C\) remains constant. If during this process the relation of pressure \(P\) and volume \(V\) is given by \(PV^n =\) constant, then n is given by (Here \(C_p\) and \(C_v\) are molar specific heat at constant pressure and constant volume, respectively) :

The decay of a proton to neutron is :

The minimum energy required by a hydrogen atom in ground state to emit radiation in Balmer series is nearly _______.

In the figure shown, after the switch \(‘S’\) is turned from position \(‘A’\) to position \(‘B’\), the energy dissipated in the circuit in terms of capacitance \(‘C’\) and total charge \(‘Q’\) is

A body is in simple harmonic motion with time period half second \((T\, = 0.5\, s)\) and amplitude one \(cm\, (A\,= 1\, cm)\). Find the average velocity in the interval in which it moves form equilibrium position to half of its amplitude .... \(cm/s\)

A ring and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of both bodies are identical and the ratio of their kinetic energies is \(\frac{7}{\mathrm{x}}\) where \(\mathrm{x}\) is___________.

The orbital angular momentum of a satellite is \(L\), when it is revolving in a circular orbit at height \(h\) from earth surface. If the distance of satellite from the earth centre is increased by eight times to its initial value, then the new angular momentum will be \(............\,L\)

Two radioactive elements \(A\) and \(B\) initially have same number of atoms. The half life of \(A\) is same as the average life of \(B\). If \(\lambda_A\) and \(\lambda_B\) are decay constants of \(A\) and \(B\) respectively, then choose the correct relation from the given options.

Two identical springs of spring constant \('2k'\) are attached to a block of mass \(m\) and to fixed support (see figure). When the mass is displaced from equilibrium position on either side, it executes simple harmonic motion. The time period of oscillations of this sytem is ...... .