Pressure inside a soap bubble is greater than the pressure outside by an amount _______. (given : \(\mathrm{R}=\) Radius of bubble, \(\mathrm{S}=\) Surface tension of bubble)

In the given circuit, the breakdown voltage of the Zener diode is \(3.0 \mathrm{~V}\). What is the value of \(\mathrm{I}_z\) ?

Let \(\left| {{{\vec A}_1}} \right| = 3,\,\left| {\vec A_2} \right| = 5\), and \(\left| {{{\vec A}_1} + {{\vec A}_2}} \right| = 5\). The value of \(\left( {2{{\vec A}_1} + 3{{\vec A}_2}} \right)\cdot \left( {3{{\vec A}_1} - 2{{\vec A}_2}} \right)\) is

The image of an object placed in air formed by a convex refracting surface is at a distance of \(10\, m\) behind the surface. The image is real and is at \(\frac{2}{3}\) of the distance of the object from the surface . The wavelength of light inside the surface is \(\frac{2}{3}\) times the wavelength in air. The radius of the curved surface is \(\frac{ x }{13}\, m\). the value of \(^{\prime} x^{\prime}\) is ....... .

A submarine experiences a pressure of \(5.05\times 10^6\,Pa\) at a depth of \(d_1\) in a sea. When it goes further to a depth of \(d_2,\) it experiences a pressure of \(8.08\times 10^6\,Pa.\) Then \(d_2 -d_1\) is approximately ........ \(m\) (density of water \(= 10^3\,kg/m^3\) and acceleration due to gravity \(= 10\,ms^{-2}\) )

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 wire carrying current \(I\) is tied between points \(P\) and \(Q\) and is in the shape of a circular arc of radius \(R\) due to a uniform magnetic field \(B\) (perpendicular to the plane of the paper, shown by \(\times \times \times \)) in the vicinity of the wire. If the wire subtends an angle \(2\theta_0\) at the centre of the circle (of which it forms an arc) then the tension in the wire is

A trransistor is connected in common emitter circuit configuration, the collector supply voltage is \(10 \,{V}\) and the voltage drop across a resistor of \(1000\, \Omega\) in the collector circuit is \(0.6\, {V}\). If the current gain factor \((\beta)\) is \(24\) , then the base currect is \(....\,\mu\) \(A.\) (Round off to the Nearest Integer)

In the given figure the magnetic flux through the loop increases according to the relation \(\phi_{B}(t)=10 t^{2}+20 t\), where \(\phi_{B}\) is in milliwebers and \(t\) is in seconds. The magnitude of current through \({R}=2 \,\Omega\) resistor at \({t}=5\, {s}\) is \(....\,{mA}\).

A body \(A,\) of mass \(m=0.1\; kg\) has an initial velocity of \(3 \hat{\mathrm{i}}\; \mathrm{ms}^{-1} .\) It collides elastically with another body, \(\mathrm{B}\) of the same mass which has an initial velocity of \(5 \hat{\mathrm{j}} \;\mathrm{ms}^{-1}\). After collision. A moves with a velocity \(\overline{\mathrm{v}}=4(\hat{\mathrm{i}}+\hat{\mathrm{j}})\). The energy of \(\mathrm{B}\) after collision is written as \(\frac{\mathrm{x}}{10} \;\mathrm{J}\) The value of \(x\) is

A parallel plate air capacitor is connected to a battery. The plates are pulled apart at uniform speed \(v\). If \(x\) is the separation between the plates at any instant, then the time rate of change of electrostatic energy of the capacitor is proportional to \(x^\alpha\), where \(\alpha\) is _____.