31.

Two oscillating simple pendululs with time periods T and $\frac{5\mathrm{T}}{4}$ are in phase at a given time. They are again in phase after an elapse of time

• 4 T

• 3 T

• 6 T

• 5 T

A wave of frequency 500 Hz travels with a speed of 360 ms^-1. The distance between two nearest points which are 60° out of phase is 

• 12 cm

• 18 cm

• 50 cm

• 24 cm

The apparent frequency observed by a moving observer away from a stationary source is 20% less than the actual frequency. If the velocity of sound in air is 330 ms^-1, then the velocity of the observer is

• 660 ms^-1

• 330 ms^-1

• 66 ms^-1

• 33 ms^-1

A string under tension of 129.6 N produces 10 beats/second, when it vibrates along with a tuning fork. When the tension in the string is increased to 160 N, it vibtrates in unison with the tuning fork. Then, frequency of the tuning fork is

• 100 Hz

• 110 Hz

• 90 Hz

• 220 Hz

An electric dipole of moment µ of 400 µC m is placed in a transverse electric field (E) of 50 Vm^-1 at an angle of 30° to E. Then, a torque of

• 10^-2 Nm acts along the direction E

• 10^-3 Nm acts along the direction µ

• 10^-2 Nm acts normal to both E and µ

• 10^-3 Nm acts along the direction E

A charge Q is distributed over two concentric hollow spheres of radii a and b $\left(\mathrm{a} > \mathrm{b}\right)$, so that the surface charge densities are equal. The potential at the common centre is $\frac{1}{4{\mathrm{\pi \epsilon }}_0}$ times.

• $\mathrm{Q} \left(\frac{\mathrm{a} + \mathrm{b}}{{\mathrm{a}}^2 + {\mathrm{b}}^2}\right)$

• $2\mathrm{Q} \left(\frac{\mathrm{a} + \mathrm{b}}{{\mathrm{a}}^2 + {\mathrm{b}}^2}\right)$

• Q

• $\frac{\mathrm{Q}}{2} \left(\frac{\mathrm{a} + \mathrm{b}}{{\mathrm{a}}^2 + {\mathrm{b}}^2}\right)$

The velocity acquired by a charged particle of mass m and charge Q accelerated from rest by a potential of V is

• $\frac{\mathrm{QV}}{\mathrm{m}}$

• $\sqrt{\frac{\mathrm{m}}{\mathrm{Qv}}}$

• $\sqrt{\frac{2\mathrm{QV}}{\mathrm{m}}}$

• mQV

A 5 µF capacitor is fully charged by a 12 V battery and then disconnected. If it is connected now parallel to an uncharged capacitor, the voltage across it is 3 V. Then, the capacity of the uncharged capacitor is

• 5 µF

• 25 µF

• 50 µF

• 10 µF

An electron moving with a constant velocity v along X-axis enters a uniform electric field applied along Y-axis. Then, the electron moves

• with uniform acceleration along Y-axis

• without any acceleration along Y-axis

• in a trajectory represented as y = ax²

• in a trajectory represented as y = ax

The resistivity of the material of potentiometer wire is 5 × 10^-6 Ω m and its area of cross-section is 5 × 10^-6 m m². If 0.2 A curent is flowing through the wire, then the potential through the wire, then the potential drop per metre length of the wire is 

• 0.1 Vm^-1

• 0.5 Vm^-1

• 0.25 Vm^-1

• 0.2 Vm^-1