A 3 m long wire of radius 3 mm shows an extension of 0.1 mm when loaded vertically by a mass of 50 kg in an experiment to determine Young's modulus. The value of Young's modulus of the wire as per this experiment is \(\mathrm{P} \times 10^{11} \mathrm{Nm}^{-2}\), where the value of P is: (Take \(\left.\mathrm{g}=3 \pi \mathrm{~m} / \mathrm{s}^2\right)\)

Two wires of same length and radius are joined end to end and loaded. The Young's modulii of the materials of the two wires are \(Y_{1}\) and \(Y_{2}\). The combination behaves as a single wire then its Young's modulus is:

The electric field in a region of space is given by, \(\overrightarrow E  = {E_0}\hat i + 2{E_0}\hat j\) where \(E_0\, = 100\, N/C\). The flux of the field through a circular surface of radius \(0.02\, m\) parallel to the \(Y-Z\) plane is nearly

If the electric potential at any point \((x, y, z) \,m\) in space is given by \(V =3 x ^{2}\) volt. The electric field at the point \((1,0,3) \,m\) will be ............

Due to cold weather a \(1\, {m}\) water pipe of cross-sectional area \(1\, {cm}^{2}\) is filled with ice at \(-10^{\circ} {C}\). Resistive heating is used to melt the ice. Current of \(0.5\, {A}\) is passed through \(4\, {k} \Omega\) resistance. Assuming that all the heat produced is used for melting, what is the minimum time required ? (In \({s}\)) (Given latent heat of fusion for water/ice \(=3.33 \times 10^{5}\, {J} {kg}^{-1}\), specific heat of ice \(=2 \times 10^{3}\, {J}\) \({kg}^{-1}\) and density of ice \(=10^{3}\, {kg} / {m}^{3}\)

A wedge \(Y\) with mass of \(10\) kg and all frictionless surfaces and the inclined surface making \(37°\) with horizontal. A block \(X\) with mass \(2\) kg is placed at the highest point of the wedge as shown in figure is at rest. At \(t = 0\) wedge \((Y)\) is pulled toward right with constant force \((f)\) of \(24\) N. Taking the block \(X\) at rest at \(t = 0\), the time taken by it to slide down \(8.8\) m on the slope, while \(Y\) is on the move, is _____ s.
(take \(\tan(37°) = 3/4\) and \(g = 10\) m/s\(^2\))

A particle is oscillating on the \(X-\) axis with an amplitude \(2\, cm\) about the point \(x_0 = 10\, cm\) with a frequency \(\omega \). A concave mirror of focal length \(5\,
cm\) is placed at the origin ( see figure) Identify the correct statements \((A)\) The image executes periodic motion \((B)\) The image executes non-periodic motion \((C)\) The turning points of the image are asymmetric w.r.t the image of the point at \(x =10\,cm\) \((D)\) The distance between the turning points of the oscillation of the image is \(\frac{{100}}{{21}}\)

An object is placed at a distance of \(12 \,{cm}\) from a convex lens. A convex mirror of focal length \(15 \,{cm}\) is placed on other side of lens at \(8 \,{cm}\) as shown in the figure. Image of object coincides with the object.When the convex mirror is removed, a real and inverted image is formed at a position. The distance of the image from the object will be ..... \((cm)\)

A convex lens, of focal length \(30\,cm,\)  a concave lens of focal length \(120\,cm,\) and a plane mirror are arranged as shown. For an object kept at a distance of \(60\,cm\)  from the convex lens, the final image, formed by the combination, is a real image, at a distance of

Two identical circular loops P and Q each of radius r are lying in parallel planes such that they have common axis. The current through P and Q are I and 4I respectively in clockwise direction as seen from O . The net magnetic field at O is: