If mass is written as \(\mathrm{m}=\mathrm{kc}^{\mathrm{p}} \mathrm{G}^{-1 / 2} \mathrm{~h}^{1 / 2}\) then the value of \(P\) will be _______. (Constants have their usual meaning with \(\mathrm{k}\) a dimensionless constant)

Which one is the correct option for the two different thermodynamic processes ?

Formation of real image using a biconvex lens is shown below: If the whole set up is immersed in water without disturbing the object and the screen positions, what will one observe on the screen?

A solid sphere of radius \(R\) carries a charge \((Q+q)\) distributed uniformly over its volume. A very small point like piece of it of mass \(m\) gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge \(q.\) If it acquires a speed \(v\) when it has fallen through a vertical height \(y\) (see figure), then : (assume the remaining portion to be spherical).

An alternating current is given by \(\mathrm{I}=\mathrm{I}_{\mathrm{A}} \sin \omega \mathrm{t}+\mathrm{I}_{\mathrm{B}} \cos \omega \mathrm{t}\). The r.m.s current will be ______.

The percentage increase in magnetic field (B) when space within a current carrying solenoid is filled with magnesium (magnetic susceptibility \(\left.\chi_{\mathrm{mg}}=1.2 \times 10^{-5}\right)\) is :

In the given circuit- the value of current \(I _{ L }\) will be \(mA\). (When \(R _{ L }=1 \,k\, \Omega\) )

The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plate) of mass \(4\;kg\). (The coordinates of the same are shown in figure) are

A coil of area A and N turns is rotating with angular velocity \(\omega\) in a uniform magnetic field \(\vec{B}\) about an axis perpendicular to \(\vec{B}\). Magnetic flux \(\varphi\) and induced \(\operatorname{emf} \varepsilon\) across it, at an instant when \(\vec{B}\) is parallel to the plane of coil, are :