A mass of \(10\,kg\) is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point, the rope deviated at an angle of \(45^o\) at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is ..........  \(N\) \((g = 10\,ms^{-2})\) 

The electric field between the two parallel plates of a capacitor of \(1.5 \mu \mathrm{F}\) capacitance drops to one third of its initial value in \(6.6 \mu \mathrm{s}\) when the plates are connected by a thin wire. The resistance of this wire is _______ \(\Omega\). (Given, \(\log 3=1.1)\)

The electromagnetic waves travel in a medium at a speed of \(2.0 \times 10^{8}\, m / s\). The relative permeability of the medium is \(1.0.\) The relative permittivity of the medium will be

Two stars of masses \(m\) and \(2\, m\) at a distance \(d\) rotate about their common centre of mass in free space. The period of revolution is

Given below are two statement: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A:\) If an electric dipole of dipole moment \(30 \times 10^{-5}\,Cm\) is enclosed by a closed surface, the net flux coming out of the surface will be zero. Reason \(R\) : Electric dipole consists of two equal and opposite charges. In the light of above, statements, choose the correct answer from the options given below:

Two concave refracting surfaces of equal radii of curvature and refractive index 1.5 face each other in air as shown in figure. A point object O is placed midway, between P and B . The separation between the images of \(O\), formed by each refracting surface is :

A rod of mass \(‘M’\) and length \(‘2L’\) is suspended at its middle by a wire. It exhibits torsional oscillations; If two masses each of \(‘m’\) are attached at distance \(‘L/2’\) from its centre on both sides, it reduces the oscillation frequency by \(20\%\). The value of ratio \(m/M\) is close to

A solenoid of \(1200\) turns is wound uniformly in a single layer on a glass tube \(2\,m\) long and \(0.2\,m\) in diameter. The magnetic intensity at the center of the solenoid when a current of \(2\,A\) flows through it is:

In a coil of resistance \(8 \Omega\), the magnetic flux due to an external magnetic field varies with time as \(\phi=\frac{2}{3}\left(9- t ^{2}\right)\). The value of total heat produced in the coil, till the flux becomes zero, will be \(....J\)

The activity of a radioactive material is \(6.4 \times 10^{-4}\) curie. Its half life is \(5\; days\). The activity will become \(5 \times 10^{-6}\) curie after \(.......day\)

A square loop of side \(20\, {cm}\) and resistance \(1\, \Omega\) is moved towards right with a constant speed \({v}_{0}\). The right arm of the loop is in a uniform magnetic field of \(5\, {T}\). The field is perpendicular to the plane of the loop and is going into it. The loop is connected to a network of resistors each of value \(4\, \Omega\). What should be the value of \(v_{0}\) so that a steady current of \(2\, {mA}\) flows in the loop ?

A block moving horizontally on a smooth surface with a speed of \(40\, {m} / {s}\) splits into two parts with masses in the ratio of \(1: 2\). If the smaller part moves at \(60\, {m} / {s}\) in the same direction, then the fractional change in kinetic energy is :-

A monochromatic beam of light has a frequency \(v = \frac{3}{{2\pi }} \times {10^{12}}\,Hz\) and is propagating along the direction \(\frac{{\hat i + \hat j}}{{\sqrt 2 }}\). It is polarized along the \(\hat k\) direction. The acceptable form for the magnetic field is