The rms value of conduction current in a parallel plate capacitor is \(6.9\,\mu\,A\). The capacity of this capacitor, if it is connected to \(230 V\) ac supply with an angular frequency of \(600\,rad / s\), will be \(....\,pF\)

Two short bar magnets oflength \(1\ cm\) each have magnetic moments \(1.20\ Am^2\) and \(1.00\ Am^2\) respectively. They are placed on a horizontal table parallel to each other with their \(N\) poles pointing towards the South. They have a common magnetic equator and are separated by a distance of \(20.0\ cm\). The value of the resultand horizontal magnetic induction at the mid-point \(O\) of the line joining their centres is close to  (Horizontal component of earth.s magnetic induction is \(3.6 \times  10^{-5}\) \(Wbm^{-2}\)  )

A cricket ball of mass \(0.15\, kg\) is thrown vertically up by a bowling machine so that it rises to a maximum height of \(20 \;m\) after leaving the machine. If the part pushing the ball applies a constant force \(F\) on the ball and moves horizontally a distance of \(0.2\, m\) while launching the ball, the value of \(F(\) in \(N)\) is  \(\left(g=10\, m s^{-2}\right)\)

A unit scale is to be prepared whose length does not change with temperature and remains \(20\,cm\), using a bimetallic strip made of brass and iron each of different length. The length of both components would change in such a way that difference between their lengths remains constant. If length of brass is \(40\,cm\) and length of iron will be\(...cm\) \(\left(\alpha_{\text {iron }}=1.2 \times 10^{-5} K ^{-1}\right.\) and \(\left.\alpha_{\text {brass }}=1.8 \times 10^{-5} K ^{-1}\right)\).

\(512\) identical drops of mercury are charged to a potential of \(2\, V\) each. The drops are joined to form a single drop. The potential of this drop is ......... \(V.\)

The electric field component of a monochromatic radiation is given by \(\vec E = 2{E_0}\,\hat i\,\cos\, kz\,\cos\, \omega t\) Its magnetic field \(\vec B\) is then given by

\(I _{ CM }\) is moment of inertia of a circular disc about an axis \(( CM )\) passing through its center and perpendicular to the plane of disc. \(I _{ AB }\) is it's moment of inertia about an axis \(A B\) perpendicular to plane and parallel to axis \(CM\) at a distance \(\frac{2}{3} R\) from center. Where \(R\) is the radius of the disc. The ratio of \(I _{ AB }\) and \(I _{ CM }\) is \(x: 9\). The value of \(x\) is \(........\)

At \(t=0\), a body of mass \(100\) g starts moving under the influence of a force \((5\hat{i}+10\hat{j})\) N. After \(2\) s its position is \((2x\hat{i}+5y\hat{j})\) m. The ratio \(x:y\) is ______.

A network of four resistances is connected to \(9\,V\) battery, as shown in figure. The magnitude of voltage difference between the points \(A\) and \(B\) is .......... \(V.\)

A \(30\) cm long solenoid has \(10\) turns per cm and area of \(5\) cm\(^2\). The current through the solenoid coil varies from \(2\) A to \(4\) A in \(3.14\) s. The e.m.f. induced in the coil is \(\alpha\times 10^{-5}\) V. The value \(\alpha\) is ________.

A block of mass \(10\, kg\) starts sliding on a surface with an initial velocity of \(9.8\, ms ^{-1}\). The coefficient of friction between the surface and bock is \(0.5\). The distance covered by the block before coming to rest is: [use \(g =9.8\, ms ^{-2}\) ].........\(m\)