Distance of the centre of mass of a solid uniform cone from its vertex is \(z_0\) . If the radius of its base is \(R\) and its height is \(h\) then \(z_0\) is equal to

Find the magnetic field at point \(P\) due to a straight line segment \(AB\) of length \(6\, cm\) carrying a current of \(5\, A\). (See figure) \((\mu _0 = 4p\times10^{-7}\, N-A^{-2})\)

Find the equivalent resistance between two ends of the following circuit

A bus moving along a straight highway with speed of \(72 \mathrm{~km} / \mathrm{h}\) is brought to halt within \(4 \mathrm{~s}\) after applying the brakes. The distance travelled by the bus during this time (Assume the retardation is uniform) is __________\(\mathrm{m}\).

A coil in the shape of an equilateral triangle of side \(10\, {cm}\) lies in a vertical plane between the pole pieces of permanent magnet producing a horizontal magnetic field \(20\, {mT}\). The torque acting on the coil when a current of \(0.2\, {A}\) is passed through it and its plane becomes parallel to the magnetic field will be \(\sqrt{{x}} \times 10^{-5} \,{Nm}\). The value of \({x}\) is ..... .

charge \(Q\) is uniformly distributed over a long rod \(AB\) of length \(L\) as shown in the figure. The electric potential at the point \(O\) lying at distance \(L\) from the end \(A\) is

A point charge of \(10^{-8} C\) is placed at origin. The work done in moving a point charge \(2 \mu C\) from point \(A (4,4,2) m\) to \(B (2,2,1) m\) is _________ J.

A point charge \(q = 1\ \mu\text{C}\) is located at a distance \(2\text{ cm}\) from one end of a thin insulating wire of length \(10\text{ cm}\) having a charge \(Q = 24\ \mu\text{C}\), distributed uniformly along its length, as shown in figure. Force between \(q\) and wire is _______ N.
(Use \(\frac{1}{4\pi\varepsilon_0} = 9 \times 10^9\text{ N}\cdot\text{m}^2/\text{C}^2\))

A transistor is used in an amplifier circuit in common emitter mode. If the base current changes by \(100 \,\mu A\), it brings a change of \(10 \,mA\) in collector current. If the load resistance is \(2 \,k \Omega\) and input resistance is \(1 \,k \Omega\), the value of power gain is \(x \times 10^{4}\). The value of \(x\) is_________

Two identical thin metal plates has charge \(q _{1}\) and \(q _{2}\) respectively such that \(q _{1}> q _{2}\). The plates were brought close to each other to form a parallel plate capacitor of capacitance \(C\). The potential difference between them is.

For a periodic motion represented by the equation \(Y=\sin \omega t+\cos \omega t\) The amplitude of the motion is 

At a certain place the angle of dip is \(30^{\circ}\) and the horizontal component of earth's magnetic field is \(0.5 G\). The earth's total magnetic field (in \(G\) ), at that certain place, is ................