The current in the windings of a toroid is $2.0\,A$. There are $400$ turns and the mean circumferential length is $40\,cm$. If the magnetic field inside the toroid is $1.0\,T$,the relative permeability is near to:

If the harmonic mean between the roots of $(5+\sqrt{2}) x^2-b x+(8+2 \sqrt{5})=0$ is $4$,then the value of $b$ is

$A$ thin circular ring of mass $M$ and radius $R$ is rotating about its axis with a constant angular velocity $\omega$. Two objects,each of mass $m$,are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity:

$A$ cylindrical rod with one end in a steam chamber and the other end in ice results in the melting of $0.1 \, g$ of ice per second. If the rod is replaced by another with half the length and double the radius of the first,and if the thermal conductivity of the material of the second rod is $1/4$ that of the first,the rate at which ice melts in $g/s$ will be:

The colour of the bead in the borax bead test is mainly due to the formation of:

$A$ small metal ball is suspended in a uniform electric field with the help of an insulated thread. If a high-energy $X$-ray beam falls on the ball,then the ball