A particle of mass \({m}\) is suspended from a ceiling through a string of length \(L\). The particle moves in a horizontal circle of radius \(r\) such that \({r}=\frac{{L}}{\sqrt{2}}\). The speed of particle will be:

Consider a finite insulated, uncharged conductor placed near a finite positively charged conductor. The uncharged body must have a potential

A uniform heavy rod of mass \(20\,kg\). Cross sectional area \(0.4\,m ^{2}\) and length \(20\,m\) is hanging from a fixed support. Neglecting the lateral contraction, the elongation in the rod due to its own weight is \(x \times 10^{-9} m\). The value of \(x\) is (Given. Young's modulus \(Y =2 \times 10^{11} Nm ^{-2}\) અને \(\left.g=10\, ms ^{-2}\right)\)

A wheel is rolling on a plane surface. The speed of a particle on the highest point of the rim is \(8 \mathrm{~m} / \mathrm{s}\). The speed of the particle on the rim of the wheel at the same level as the centre of wheel, will be :

Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\) Assertion \(A\) : A spherical body of radius \((5 \pm 0.1)\) \(mm\) having a particular density is falling through a liquid of constant density. The percentage error in the calculation of its terminal velocity is \(4\,\%\). Reason \(R\) : The terminal velocity of the spherical body falling through the liquid is inversely proportional to its radius. In the light of the above statements, choose the correct answer from the options given below on :

A \(12\,V\) battery connected to a coil of resistance \(6 \,\Omega\) through a switch, drives a constant current in the circuit. The switch is opened in \(1\,ms\). The emf induced across the coil is \(20 \;V\). The inductance of the coil is  ........... \(mH\)

Two satellites \(A\) and \(B\) of masses \(200\, kg\) and \(400\, kg\) are revolving round the earth at height of \(600\, km\) and \(1600\, km\) respectively. If \(T _{ A }\) and \(T _{ B }\) are the time periods of \(A\) and \(B\) respectively then the value of \(T _{ B }- T _{ A }\) [Given : radius of earth \(=6400\, km\), mass of earth \(=6 \times 10^{24}\, kg\) ]

A composite parallel plate capacitor is made up of two different dielectric materials with different thickness \(\left(t_{1}\right.\) and \(\left.t_{2}\right)\) as shown in figure. The two different dielectric material are separated by a conducting foil \(F\). The voltage of the conducting foil is \(.....V\)

Four particles each of mass \(1 \mathrm{~kg}\) are placed at four corners of a square of side \(2 \mathrm{~m}\). Moment of inertia of system about an axis perpendicular to its plane and passing through one of its vertex is_________ \(\mathrm{kgm}^2\).

A Carnot engine take \(5000 \,k\,cal\) of heat from a reservoir at \(727\,^{\circ}C\) and gives heat to a \(\operatorname{sink}\) at \(127\,^{\circ}C\). The work done by the engine is \(.......... \times 10^{6}\,J\)

An experiment is performed to determine the \(I-V\) characteristics of a Zener diode, which has a protective resistance of \(R = 100 \,\Omega ,\) and a maximum power of dissipation rating of \(1\,W\) .The minimum voltage range of the \(DC\) source in the circuit is