A block of \(\sqrt{3}\,kg\) is attached to a string whose other end is attached to the wall. An unknown force \(F\) is applied so that the string makes an angle of \(30^{\circ}\) with the wall. The tension \(T\) is \(...........\,N\) :(Given \(g =10\,ms ^{-2}\) )

Maatch Liat \(I\) List \(II\) Chose the correct answer from the options given below

Choose the incorrect statement from the following

In a coil of resistance \(100\ \Omega\) , a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is......\(Wb\)

The aperture diameter of a telescope is \(5\; \mathrm{m} .\) The separation between the moon and the earth is \(4 \times 10^{5} \;\mathrm{km} .\) With light of wavelength of \(5500\;\mathring A\), the minimum separation between objects on the surface of moon, so that they are just resolved, is close to......\(m\)

A sample of gas at temperature \(T\) is adiabatically expanded to double its volume. The work done by the gas in the process is \(\left(\right.\) given, \(\left.\gamma=\frac{3}{2}\right)\) :

Two infinite planes each with uniform surface charge density \(+\sigma\) are kept in such a way that the angle between them is \(30^{\circ} .\) The electric field in the region shown between them is given by

Two magnetic dipoles \(X\) and \(Y\) are placed at a separation \(d\), with their axes perpendicular to each other. The dipole moment of \(Y\) is twice that of \(X\). A particle of charge \(q\) is passing through their mid-point \(P\), at angle \(\theta  = 45^o\) with the horizontal line as shown in the figure. What would be the magnitude of force on the particle at that instant ? (\(d\) is much larger than the dimensions of the dipole)

A charge particle moving in magnetic field \(B\), has the components of velocity along \(B\) as well as perpendicular to \(B\). The path of the charge particle will be

Two uniform circular discs are rotating independently in the same direction around their common axis passing through their centres. The moment of inertia and angular velocity of the first disc are \(0.1 \;kg - m ^{2}\) and \(10\; rad \,s^{-1}\) respectively while those for the second one are \(0.2 \;kg - m ^{2}\) and \(5\; rad \,s ^{-1}\) respectively. At some instant they get stuck together and start rotating as a single system about their common axis with some angular speed. The Kinetic energy of the combined system is ...........\(J\)

Which of the following is not a dimensionless quantity?

A series LCR circuit with \(R = 20\ \Omega\), \(L = 1.6\text{ H}\) and \(C = 40\ \mu\text{F}\) is connected to a variable frequency a.c. source. The inductive reactance at resonant frequency is _______ \(\Omega\).

The dipole moment of a circular loop carrying a current \(I\), is \(m\) and the magnetic field at the centre of the loop is \(B_1\) . When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is \(B_2\) . The ratio \(\frac{{{B_1}}}{{{B_2}}}\) is