The fractional compression \(\left(\frac{\Delta \mathrm{V}}{\mathrm{V}}\right)\) of water at the depth of 2.5 km below the sea level is ______ \(\%\). Given, the Bulk modulus of water \(=2 \times 10^9 \mathrm{~N} \mathrm{~m}^{-2}\), density of water \(=10^3\) \(\mathrm{kg} \mathrm{m}^{-3}\), acceleration due to gravity \(=\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\).

Given that \(1\,g\) of water in liquid phase has volume \(1\,cm^3\) and in vapour phase \(1671\, cm^3\) at atmospheric pressure and the latent heat of vaporization of water is \(2256\,J/g;\) the change in the internal energy in joules for \(1\,g\) of water at \(373\,K\) when it changes from liquid phase to vapour phase at the same temperature is ....... \(J\)

A charged particle carrying charge \(1\,\mu C\) is moving with velocity \((2 \hat{ i }+3 \hat{ j }+4 \hat{ k })\, ms ^{-1} .\) If an external magnetic field of \((5 \hat{ i }+3 \hat{ j }-6 \hat{ k }) \times 10^{-3}\, T\) exists in the region where the particle is moving then the force on the particle is \(\overline{ F } \times 10^{-9} N\). The vector \(\overrightarrow{ F }\) is :

Two bodies of mass \(4 \mathrm{~g}\) and \(25 \mathrm{~g}\) are moving with equal kinetic energies. The ratio of magnitude of their linear momentum is :

A uniform thin metal plate of mass \(10 \mathrm{~kg}\) with dimensions is shown. The ratio of \(x\) and \(y\) coordinates of center of mass of plate in \(\frac{n}{9}\). The value of \(n\) is _______.

A plano-convex lens (focal length \(f_2,\) refractive index \(\mu _2,\) radius of curvature \(R\) ) fits exactly into a plano-concave lens (focal length \(f_1,\) refractive index \(\mu _1,\) radius of curvature \(R\) ). Their plane surfaces are parallel to each other. Then, the focal length of the combination will be

A vessel with square cross-section and height of 6 m is vertically partitioned. A small window of \(100 \mathrm{~cm}^2\) with hinged door is fitted at a depth of 3 m in the partition wall. One part of the vessel is filled completely with water and the other side is filled with the liquid having density \(1.5 \times 10^3 \mathrm{~kg} / \mathrm{m}^3\). What force one needs to apply on the hinged door so that it does not get opened ?
(Acceleration due to gravity \(=10 \mathrm{~m} / \mathrm{s}^2\))

A \(20\,cm\) long metallic rod is rotated with \(210\,rpm\) about an axis normal to the rod passing through its one end. The order end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field \(0.2\,T\) parallel to the axis exists everywhere. The emf developed between the centre and the ring is \(.......\,mV\).Take \(\pi=\frac{22}{7}\)

In the below circuit the current in each resistance is