A capillary tube when immersed vertically in water, the rise of water column is upto height $h_1$ on earth's surface. When this arrangement is taken into a mine of depth 'd', below earth's surface, the height of the water column is $\mathrm{h}_2$. If R is the radius of the earth, the ratio $\frac{\mathrm{h}_2}{\mathrm{~h}_1}$ is

The work done in turning a magnet of magnetic moment ' $M$ ' by an angle of $90^{\circ}$ from the meridian is ' $n$ ' times the corresponding Work done to turn it through an angle of $60^{\circ}$ where the value of ' $n$ ' is $\left(\cos 90^{\circ}=0, \cos 60^{\circ}=0.5\right)$

When magnetic flux changes from $6.5 \times 10^{-2} \mathrm{~Wb}$ to $11 \times 10^{-2} \mathrm{~Wb}$ and the change in current is 0.03 A , the coefficient of mutual inductance will be

At a place, the length of the oscillating simple pendulum is made $\frac{1}{4}$ times keeping amplitude same then the total energy will be