As shown in the figure, a particle is moving with constant speed \(\pi\,m / s\). Considering its motion from \(A\) to \(B\), the magnitude of the average velocity is:

In a fluorescent lamp choke (a small transformer) \(100 \;\mathrm{V}\) of reverse voltage is produced when the choke current changes uniformly from \(0.25 \;\mathrm{A}\) to \(0\;\mathrm{A}\) in a duration of \(0.025 \;\mathrm{ms} .\) The self-inductance of the choke (in \(\mathrm{mH})\) is estimated to be

Two charged conducting spheres \(S_1\) and \(S_2\) of radii \(8\) cm and \(18\) cm are connected to each other by a wire. After equilibrium is established, the ratio of electric fields on \(S_1\) and \(S_2\) spheres are \(E_{S_1}\) and \(E_{S_2}\) respectively. The value of \(\dfrac{E_{S_1}}{E_{S_2}}\) is _______.

Two identical spheres each of mass \(2 \mathrm{~kg}\) and radius \(50 \mathrm{~cm}\) are fixed at the ends of a light rod so that the separation between the centers is \(150 \mathrm{~cm}\). Then, moment of inertia of the system about an axis perpendicular to the rod and passing through its middle point is \(\frac{x}{20} \mathrm{~kg} \mathrm{~m}^2\), where the value of \(\mathrm{x}\) is _______.

A sample of gas at temperature \(\mathrm{T}\) is adiabatically expanded to double its volume. Adiabatic constant for the gas is \(\gamma=3 / 2\). The work done by the gas in the process is _______. \((\mu=1 \mathrm{~mole})\)

Three force \(F_1=10\,N , F_2=8\,N , F _3=6\,N\) are acting on a particle of mass \(5\,kg\). The forces \(F _2\) and \(F _3\) are applied perpendicular so that particle remains at rest. If the force \(F_1\) is removed, then the acceleration of the particle is \(......ms^{-2}\)

An electron with kinetic energy \(K _{1}\) enters between parallel plates of a capacitor at an angle \('\alpha'\) with the plates. It leaves the plates at angle \(' \beta '\) with kinetic energy \(K _{2}\). Then the ratio of kinetic energies \(K _{1}: K _{2}\) will be ....... .

Figure below shows a liquid being pushed out of the tube by a piston having area of cross section \(2.0\,cm ^2\). The area of cross section at the outlet is \(10\,mm ^2\). If the piston is pushed at a speed of \(4\,cm s ^{-1}\), the speed of outgoing fluidis \(.........\,cm s ^{-1}\).

If \(\mu_0\) and \(\varepsilon_0\) are the permeability and permittivity of free space, respectively, then the dimension of \(\left(\frac{1}{\mu_0 \varepsilon_0}\right)\) is :

Two coherent monochromatic light beams of intensities 4I and 9I are superimposed. The difference between the maximum and minimum intensities in the resulting interference pattern is xI. The value of \(x\) is ______.

A rod of length \(10\) cm lies along the principle axis of a concave mirror of focal length \(10\) cm as shown in figure. The length of the image is _____ cm.