Show that when a string fixed at two ends vibrates in 1 loops,2 loops,3 loops and 4 loops, the frequencies are in the ratio 1:2:3:4.

Two cones have their heights in the ratio 1:3 and the radii of their bases in the ratio 3:1. show that their volumes are in the ratio 3:1.

A rectangular loop of wire of size 4 cm xx 10 cm carries a steady current of 2A. A straight long wire carrying 5A current is kept near the loop If the loop and the wire are coplanar, find (i) the torque acting on the loop and (ii) the magnitude and direction of the force on the loop due to the current carrying wire(fig).

The two parallel circular loops of wire shown in fig each have a radius R = 20 cm and are separated by a distance a = 0.5 cm. The bottom loop is held fixed and the top loop hangs from one end of the arm of an equal arm balance. Since a is much smaller than R, the magnetic field produced by one loop at the other is practically the same as if both were long straight wires. if the curret in each loop is 20 A, how big is the force of attraction of one loop for the other?

The figure shows certain wire segments joined together to form a coplanar loop. The loop is placed in a perpendicular magnetic field in the direction going into the plane of the figure. The magnitude of the field increases with time I_(1) and I_(2) are the currents in the segments ab and cd. Then,

A thin circular loop of radius R rotates about its vertical diameter with an angular frequency omega . Show that a small bead on the wire loop rem ains at its lowermost point for omega oversetlarrsqrt(g/R) What is the angle made by the radius vector joining the centre to the bead with the vertical downward direction for omega = sqrt (2g/R) ? neglect friction.

A wire stretched between two rigid supports vibrates in itsfundamental mode with a frequency of 45 Hz. The mass of the wire is 3.5 xx 10^-2 kg and itslinear mass density is 4.0 xx 10^-2 kg m^-1 . What is the tension in the string?

A wire stretched between two rigid supports vibrates in itsfundamental mode with a frequency of 45 Hz. The mass of the wire is 3.5 xx 10^-2 kg and itslinear mass density is 4.0 xx 10^-2 kg m^-1 . What is the speed of a transverse wave on the string

Show that the three points A(2,3,4) and B(-1,2,-3) and C(-4,1,-10) are collinear and find the ratio in which C divides [AB].

A rectangular loop of sides 8 cm and 2 cm with a small cut is moving out of a region of uniform magnetic field of magntude 0.3 T directed normal to the loop. What is the voltage developed acros the cut, if the velocity of the loop is 1 cms^-1 in a diretion normal to the shorter side of the loop. For how long does the induced voltage last in each case?

A wire 88cm long bent into a circular loop is placed perpendicular to the magnetic field of density 2.5 Wb m^(-2) . Within 0.5 s the loop is changed into square of each side 22 cm and the density is increased to 3Wbm-2 . Calculate the value of e.m.f. induced.