A uniform cable of mass \(‘M’\) and length \(‘L’\) is placed on a horizontal surface such that its \({\left( {\frac{1}{n}} \right)^{th}}\)  part is hanging below the edge of the surface. To lift the hanging part of the cable upto the surface, the work done should be

The electric current in a circular coil of four turns produces a magnetic induction \(32\,T\) at its centre. The coil is unwound and is rewound into a circular coil of single turn, the magnetic induction at the centre of the coil by the same current will be \(..........\,T\)

A square shaped hole of side \(l=\frac{a}{2}\) is carved out at a distance \(d =\frac{ a }{2}\) from the centre \('O'\) of a uniform circular disk of radius \(a\). If the distance of the centre of mass of the remaining portion from \(O\) is \(-\frac{a}{X},\) value of \(X\) (to the nearest integer) is.......

Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A\) : Body \('P'\) having mass \(M\) moving with speed \('u'\) has head-on collision elastically with another body \('Q'\) having mass \('m'\) initially at rest. If \(m< < M,\) body \('Q'\) will have a maximum speed equal to \('2u'\) after collision. Reason \(R\) : During elastic collision, the momentum and kinetic energy are both conserved. In the light of the above statements, choose the most appropriate answer from the options given below:

A spherical body of mass \(2\,kg\) starting from rest acquires a kinetic energy of \(10000\,J\) at the end of \(5^{\text {th }}\) second. The force acted on the body is \(.....N\)

A parallel beam of monochromatic light of wavelength \(600 \mathrm{~nm}\) passes through single slit of \(0.4 \mathrm{~mm}\) width. Angular divergence corresponding to second order minima would be _______ \(\times 10^{-3} \mathrm{rad}\).

The relative permittivity of distilled water is \(81 .\) The velocity of light in it will be \(....\,\times 10^{7}\,{m} / {s}\) \(\left(\right.\) Given \(\left.\mu_{r}=1\right)\)

According to Bohr's theory, the moment of momentum of an electron revolving in \(4^{\text {th }}\) orbit of hydrogen atom is _______.

If the distance of the earth from Sun is \(1.5 \times 10^6\,km\). Then the distance of an imaginary planet from Sun, if its period of revolution is \(2.83\) years is \(.............\times 10^6\,km\)

A rectangular coil (Dimension \(5\,cm\times 2\,cm\) ) with \(100\,turns,\) carrying a current of \(3\,A\) in the clock-wise direction, is kept centered at the origin and in the \(X-Z\) plane. A magnetic field of \(1\,T\) is applied along \(X-\) axis. If the coil is tilted through \(45^o\) about \(Z-\) axis, then the torque on the coil is.....\(Nm\)

A cubical block of side \(0.5\,m\) floats on water with \(30\%\) of its volume under water. ....... \(kg\) is the maximum weight that can be put on the block without fully submerging it under water ? [Take density of water \(= 10^3\,kg/m^3\) ]

person trying to lose weight by burning fat lifts a mass of \(10\ kg\) upto a height of \(1\ m\) \(1000\) times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up? Fat supplies \(3.8 \times 10^7\ J\) of energy per kg which is converted to mechanical energy with a \(20\%\) efficiency rate. Take \(g=9.8\) \(ms^{-2}\)