Two wires of the same material and length but diameters in the ratio $1:2$ are stretched by the same force. The elastic potential energy per unit volume for the wires, when stretched by the same force, will be in the ratio: (in $:1$)

Honey bees also produce beeswax,which finds many uses in industry,such as:

There is an error of $\pm 0.04 \text{ cm}$ in the measurement of the diameter of a sphere. When the radius is $10 \text{ cm}$,the percentage error in the volume of the sphere is

As shown in the figure,a block of mass $10 \, kg$ lying on a horizontal surface is pulled by a force $F$ acting at an angle of $30^{\circ}$ with the horizontal. For $\mu_{s} = 0.25$,the block will just start to move for the value of $F$ in $N$ is: [Given $g = 10 \, ms^{-2}$]

$A$ pendulum is oscillating with frequency $n$ on the surface of the earth. It is taken to a depth $d = \frac{R}{2}$ below the surface of the earth. What is the new frequency of oscillation at this depth? [$R$ is the radius of the earth]

$A$ steady current flows in a long wire. It is bent into a circular loop of one turn and the magnetic field at the centre of the coil is $B$. If the same wire is bent into a circular loop of $n$ turns,the magnetic field at the centre of the coil is