Water is flowing in a conical tube as shown in figure. Velocity of water at area ' $\mathrm{A}_2$ ' is $60 \mathrm{~cm} / \mathrm{s}$. The value of ' $\mathrm{A}_1$ ' and ' $\mathrm{A}_2$ ' is $10 \mathrm{~cm}^2$ and $5 \mathrm{~cm}^2$ respectively. The pressure difference at both the cross-section is

A point object kept at P in front of a glass sphere of radius ' $R$ ' has its image formed at $Q$ such that $\mathrm{PO}=\mathrm{QO}$. The refractive index of material of glass sphere is 1.4. The distance PO is equal to

The magnetic flux through a coil of resistance ' $R$ ' changes by an amount ' $\Delta \phi$ ' in time ' $\Delta t$ '. The amount of induced current and induced charge in the coil are respectively

A circular disc of radius ' $R$ ' and thickness $\frac{R}{8}$ has moment of inertia 'I' about an axis passing through its centre and perpendicular to its plane. It is melted and recasted into a solid sphere then moment of inertia of sphere about an axis passing through diameter is