A particle of mass \(0.50 \mathrm{~kg}\) executes simple harmonic motion under force \(\mathrm{F}=-50\left(\mathrm{Nm}^{-1}\right) \mathrm{x}\). The time period of oscillation is \(\frac{x}{35} s\). The value of \(x\) is _______. (Given \(\pi=\frac{22}{7}\) )

An inductor coil stores \(64\, {J}\) of magnetic field energy and dissipates energy at the rate of \(640\, {W}\) when a current of \(8\, {A}\) is passed through it. If this coil is joined across an ideal battery, find the time constant of the circuit in seconds

\(AC\) voltage \(V(t)=20\,sin\omega \,t\) of frequency \(50\, {Hz}\) is applied to a parallel plate capacitor. The separation between the plates is \(2\, {mm}\) and the area is \(1 \,{m}^{2}\). The amplitude of the oscillating displacement current for the applied \(AC\) voltage is ...... \(\mu {A}\). [Take \(\left.\varepsilon_{0}=8.85 \times 10^{-12} \,{F} / {m}\right]\)

The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by \(0.02 \%\) is ______ \(\mathrm{m}\). (Take density of sea water \(=10^3 \mathrm{kgm}^{-3}\), Bulk modulus of rubber \(=9 \times 10^8 \mathrm{Nm}^{-2}\), and \(\mathrm{g}=10 \mathrm{~ms}^{-2}\) )

The photodiode is used to detect the optiocal signals. These diodes are preferably operated in reverse biased mode because.

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:

Two moles a monoatomic gas is mixed with six moles of a diatomic gas. The molar specific heat of the mixture at constant volume is _______.

A wind-10.Powered generator converts wind energy into electrical energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed \(v\), the electrical 10.Power output will be most likely proportional to

A particle of mass \(\mathrm{m}\) is fixed to one end of a light spring having force constant \(\mathrm{k}\) and unstretched length \(\ell .\) The other end is fixed. The system is given an angular speed \(\omega\) about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is

A telescope with objective diameter \(R\) is used to observe a distant star emitting light of wavelength \(500\) nm, at a resolution of \(5 \times 10^{-7}\) radian. The value of \(R\) is _____ cm.