A small liquid drop of radius \(R\) is divided into \(27\) identical liquid drops. If the surface tension is \(\mathrm{T}\), then the work done in the process will be _______.

A hole is drilled in a metal sheet. At \(27^{\circ} C\), the diameter of hole is 5 cm . When the sheet is heated to \(177^{\circ} C\), the change in the diameter of hole is \(d \times 10^{-3} cm\). The value of \(d\) will be ________ , if coefficient of linear expansion of the metal is \(1.6 \times 10^{-5} /{ }^{\circ} C\)

Two inclined planes are placed as shown in figure. A block is projected from the Point \(A\) of inclined plane \(A B\) along its surface with a velocity just sufficient to carry it to the top Point \(B\) at a height \(10 m\). After reaching the Point \(B\) the block slides down on inclined plane \(BC\). Time it takes to reach to the point \(C\) from point \(A\) is \(t (\sqrt{2}+1) s\). The value of \(t\) is........(use \(g =10 m / s ^{2}\) )

A closed vessel contains \(0.1\) mole of a monoatomic ideal gas at \(200\, K\). If \(0.05\) mole of the same gas at \(400\, K\) is added to it, the final  equilibrium temperature (in \(K\) ) of the gas in the vessel will be closed to

An inclined plane making an angle of \(30^{\circ}\) with the horizontal is placed in a uniform horizontal electric field \(200 \, \frac{ N }{ C }\) as shown in the figure. A body of mass \(1\, kg\) and charge \(5\, mC\) is allowed to slide down from rest at a height of \(1\, m\). If the coefficient of friction is \(0.2,\) find the time (in \(s\) )taken by the body to reach the bottom. \(\left[ g =9.8 \,m / s ^{2}, \sin 30^{\circ}=\frac{1}{2}\right.\); \(\left.\cos 30^{\circ}=\frac{\sqrt{3}}{2}\right]\)

A drop of liquid of density \(\rho\) is floating half immersed in a liquid of density \(\sigma\) and surface tension \(7.5 \times 10^{-4}\,N\,cm ^{-1}\). The radius of drop in \(cm\) will be : (Take : \(g =10\,m / s ^{2}\) )

Three identical bars \(A, B\) and \(C\) are made of different magnetic materials. When kept in a uniform magnetic field, the field lines around them look as follows: Make the correspondence of these bars with their material being diamagnetic \((D)\), ferromagnetic \((F)\) and paramagnetic \((P)\)

As shown in the figure, two parallel plate capacitors having equal plate area of \(200\,cm ^2\) are joined in such a way that \(a \neq b\). The equivalent capacitance of the combination is \(x \varepsilon_0 F\). The value of \(x\) is \(..........\).

A string is clamed at both the ends and it is vibrating in its \(4^{th}\) harmonic. The equation of the stationary wave is \(Y =0.3\,sin\,(0.157\,x) \,cos\,(200\pi t)\). The length of the string is ..... \(m\) (all quantities are in \(SI\) units)

A \(16\, \Omega\) wire is bend to form a square loop. A \(9 \,{V}\) supply having internal resistance of \(1 \,\Omega\) is connected across one of its sides. The potential drop across the diagonals of the square loop is \(.......\,\times 10^{-1} \,{V}\)

An air bubble of radius 1.0 mm is observed at a depth of 20 cm below the free surface of a liquid having surface tension \(0.095 \mathrm{~J} / \mathrm{m}^2\) and density \(10^3 \mathrm{~kg} / \mathrm{m}^3\). The difference between pressure inside the bubble and atmospheric pressure is _____ \(\mathrm{N} / \mathrm{m}^2\). (Take \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\) )

An \(emf\) of \(0.08\,V\) is induced in a metal rod of length \(10\,cm\) held normal to a uniform magnetic field of \(0.4\,T\), when moves with a velocity of ...........\(ms^{-1}\)