Two particles \(A, B\) are moving on two concentric circles of radii \(R_1\) and \(R_2\) with equal angular speed \(\omega \). At \(t = 0,\) their positions and direction of motion are shown in the figure The relative velocity \(\overrightarrow {{V_A}}  - \overrightarrow {{V_B}} \) at \(t = \frac{\pi }{{2\omega }}\) is given by

A coil is placed in a magnetic field \(\overrightarrow{{B}}\) as shown below: A current is induced in the coil because \(\overrightarrow{{B}}\) is:

For the series LCR circuit connected with 220 V , 50 Hz a.c source as shown in the figure, the power factor is \(\frac{\alpha}{10}\). The value of \(\alpha\) is _________

The relative error in the determination of the surface area of a sphere is \(\alpha \). Then the relative error in the determination of its volume is

Two resistors of \(100 \Omega\) each are connected in series with a 9 V battery. A voltmeter of \(400 \Omega\) resistance is connected to measure the voltage drop across one of the resistors. The voltmeter reading is _________ V.

Proton \((P)\) and electron \((e)\) will have same deBroglie wavelength when the ratio of their momentum is (assume, \(m _{ p }=1849\,m _{ e }\))

Two \(10 \; cm\) long, straight wires, each carrying a current of \(5 \; A\) are kept parallel to each other. If each wire experienced a force of \(10^{-5} \; N\), then separation between the wires is \(\dots \; cm\).

A uniform rod of length \('l'\) is pivoted at one of its ends on a vertical shaft of negligible radius When the shaft rotates at angular speed \(\omega\) the rod makes an angle \(\theta\) with it (see figure). To find \(\theta\) equate the rate of change of angular momentum (direction going into the paper ) \(\frac{ m \ell^{2}}{12} \omega^{2} \sin \theta \cos \theta\) about the centre of mass \((CM)\) to the torque provided by the horizontal and vertical forces \(F_{H}\) and \(F_{V}\) about the CM. The value of \(\theta\) is then such that:

The charge on capacitor of capacitance \(15 \mu F\) in the figure given below is \(\dots \; \mu c\)