Two identical piano wires, kept under the same tension T, have a fundamental frequency of 600 Hz. The fractional increase in the tension of one of the wires which will lead to the occurrence of 6 beats/s when both the wires oscillate together would be:

1. 0.01

2. 0.02

3. 0.03

4. 0.04

A thin prism of angle \(15^\circ\) made of glass of refractive index \(\mu_1=1.5\) is combined with another prism of the glass of refractive index \(\mu_1=1.75.\) The combination of the prism produced dispersion without deviation. The angle of the second prism should be:
1. \(5^\circ\)
2. \(7^\circ\)
3. \(10^\circ\)
4. \(12^\circ\)

A converging beam of rays is incident on a diverging lens. Having passed through the lens the rays intersect at a point \(15~\text{cm}\) from the lens on the opposite side. If the lens is removed the point where the rays meet will move \(5~\text{cm}\) closer to the lens. The focal length of the lens is:
1.  \(5~\text{cm}\)
2. \(-10~\text{cm}\)
3. \(20~\text{cm}\)
4. \(-30~\text{cm}\)

Three charges, each \(+q\), are placed at the corners of an equilateral triangle \(ABC\) of sides \(BC\), \(AC\), and \(AB\). \(D\) and \(E\) are the mid-points of \(BC\) and \(CA\). The work done in taking a charge \(Q\) from \(D\) to \(E\) is:

In the circuit shown in the figure below, if the potential at point \(A\) is taken to be zero, the potential at point \(B\) will be:

1. \(+1\) V
2. \(-1\) V
3. \(+2\) V
4. \(-2\) V

A thermocouple of negligible resistance produces an e.m.f. of 40 µV/ºC in the linear range of temperature. A galvanometer of resistance 10 ohm whose sensitivity is 1 µA/division, is employed with the thermocouple. The smallest value of temperature difference that can be detected by the system will be:
1. 0.25ºC
2. 0.5 ºC
3. 1ºC
4. 0.1ºC

Charge q is uniformly spread on a thin ring of radius R. The ring rotates about its axis with a uniform frequency of f Hz. The magnitude of magnetic induction at the centre of the ring is:

1. $\frac{{\mathrm{\mu }}_0\mathrm{qf}}{2\mathrm{\pi R}}$

2. $\frac{{\mathrm{\mu }}_0\mathrm{qf}}{2\mathrm{R}}$

3. $\frac{{\mathrm{\mu }}_0\mathrm{q}}{2\mathrm{fR}}$

4. $\frac{{\mathrm{\mu }}_0\mathrm{q}}{2\mathrm{\pi fR}}$

A short bar magnet of magnet moment \(0.4\) ${\mathrm{JT}}^{-1}$ is placed in a uniform magnetic field of \(0.16\) $\mathrm{T}$. The magnet is in stable equilibrium when the potential energy is:
1. \(0.064\) J
2. \(-0.064\) J
3. zero
4.\(-0.082\) J