The magnetic moment of a current (I) carrying circular coil of radius '$$r$$' and number of turns '$$n$$' depends on

A spherical drop of liquid splits into 1000 identical spherical drops. If '$$\mathrm{E}_1$$' is the surface energy of the original drop and '$$\mathrm{E}_2$$' is the total surface energy of the resulting drops, then $$\frac{E_1}{E_2}=\frac{x}{10}$$. Then value of '$$x$$' is

The displacement of two sinusoidal waves is given by the equation

$$\begin{aligned} & \mathrm{y}_1=8 \sin (20 \mathrm{x}-30 \mathrm{t}) \\ & \mathrm{y}_2=8 \sin (25 \mathrm{x}-40 \mathrm{t}) \end{aligned}$$

then the phase difference between the waves after time $$t=2 \mathrm{~s}$$ and distance $$x=5 \mathrm{~cm}$$ will be

$$I_1$$ is the moment of inertia of a circular disc about an axis passing through its centre and perpendicular to the plane of disc. $$I_2$$ is its moment of inertia about an axis $$A B$$ perpendicular to plane and parallel to axis $$\mathrm{CM}$$ at a distance $$\frac{2 R}{3}$$ from centre. The ratio of $$I_1$$ and $$I_2$$ is $$x: 17$$. The value of '$$x$$' is (R = radius of the disc)