Seven identical circular planar disks, each of mass \(M\) and radius \(R\) are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point \(P\) is:

An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency \(10\ GHz\). What is the frequency of the microwave measured by the observer?.......\(GHz\) ( speed of light \(= 3 \times  10^8 \) \(ms^{-1}\))

A capacitor \(C _{1}\) of capacitance \(5\,\mu F\) is charged to a potential of \(30\,V\) using a battery. The battery is then removed and the charged capacitor is connected to an uncharged capacitor \(C _{2}\) of capacitance \(10\,\mu F\) as shown in figure. When the switch is closed charge flows between the capacitors. At equilibrium, the charge on the capacitor \(C _{2}\) is________ \(\mu C\)

A stationary observer receives sound from two identical tuning forks, one of which approaches and the other one recedes with the same speed (much less than the speed of sound). The observer hears \(2\; beats/sec\). The oscillation frequency of each tuning fork is \(v_{0}=1400 \;\mathrm{Hz}\) and the velocity of sound in air is \(350\; \mathrm{m} / \mathrm{s}\). The speed of each tuning fork is close to 

What is the half-life (in years) period of a radioactive material if its activity drops to \(1 / 16^{\text {th }}\) of its initial value of \(30\) years?

The electrostatic potential on the surface of uniformly charged spherical shell of radius \(\mathrm{R}=10 \mathrm{~cm}\) is 120 V. The potential at the centre of shell, at a distance \(\mathrm{r}=5 \mathrm{~cm}\) from centre, and at a distance \(\mathrm{r}=15 \mathrm{~cm}\) from the centre of the shell respectively, are :

A body of mass \(M\) and charge \(q\) is connected to a spring of spring constant \(k\). It is oscillating along \(x-\) direction about its equilibrium position, taken to be at \(x = 0\), with an amplitude \(A\). An electric field \(E\) is applied along the \(x-\) direction. Which of the following statements is correct?

Determine the electric dipole moment of the system of three charges, placed on the vertices of an equilateral triangle, as shown in the figure

An alternating current is represented by the equation, \(i=100 \sqrt{2} \sin (100 \pi t)\) ampere. The RMS value of current and the frequency of the given alternating current are ________.

For full scale deflection of total \(50\) divisions, \(50\,{mV}\) voltage is required in galvanometer. The resistance of galvanometer if its current sensitivity is \(2\, {div} / {mA}\) will be \(.....\Omega\)

When the displacement of a simple harmonic oscillator is one third of its amplitude, the ratio of total energy to the kinetic energy is \(\frac{x}{8}\), where \(x=\) _______.