A metal rod of 50 cm length is clamped at its midpoint and is set to vibrations. The density of that metal is \( 2 \times 10^3 \, {kg/m}^3 \).Young's modulus of that metal is \( 8 \times 10^8 \, {Nm}^2 \). The fundamental frequency of the vibration is
The relation between velocity \( V \) (in ms\(^{-1}\)) and the displacement \( x \) (in meters) of a particle in motion is \( 2V = \sqrt{37 + 32x} \). The acceleration of the particle is
If the input frequency is 50 Hz, the output frequency of a full wave rectifier is:
A current-carrying coil experiences a torque due to a magnetic field. The value of the torque is 80% of the maximum possible torque. The angle between the magnetic field and the normal to the plane of the coil is
A wire shaped in a regular hexagon of side 2 cm carries a current of 4 A. The magnetic field at the centre of the hexagon is.