If the gravitational field in the space is given as \(\left(-\frac{ K }{ r ^2}\right)\). Taking the reference point to be at \(r =2\,cm\) with gravitational potential \(V =10\,J / kg\). Find the gravitational potential at \(r =3\,cm\) in \(SI\) unit (Given, that \(K =6\,J cm / kg\) )

A particle of charge \(q\) and mass \(m\) is moving with a velocity \(-v \hat{ i }(v \neq 0)\) towards a large screen placed in the \(Y - Z\) plane at a distance \(d.\) If there is a magnetic field \(\overrightarrow{ B }= B _{0} \hat{ k },\) the minimum value of \(v\) for which the particle will not hit the screen is

The top of a water tank is open to air and its water level is maintained. It is giving out \(0.74\,m^3\) water per minute through a circular opening of \(2\,cm\) radius in its wall. The depth of the centre of the opening from the level of water in the tank is close to........ \(m\)

Consider two \(npn\) transistors as shown in figure. If \(0\,Volts\) corresponds to false and \(5\, Volts\) correspond to true then the output at \(C\) corresponds to

The magnetic susceptibility of a material of a rod is \(499 .\) Permeability in vaccum is \(4 \pi \times 10^{-7}\; {H} / {m}\). Absolute permeability of the material of the rod is \(....\,\pi \times 10^{-4} {H} / {m}\)

The escape velocity from a spherical planet A is 10 km/s. The escape velocity from another planet B whose density and radius are 10% of those of planet A, is __________ m/s.

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason \(R\). Assertion A : Efficiency of a reversible heat engine will be highest at \(-273^{\circ} C\) temperature of cold reservoir. Reason \(R\) : The efficiency of Carnot's engine depends not only on temperature of cold reservoir but it depends on the temperature of hot reservoir too and is given as \(\eta=\left(1-\frac{ T _2}{ T _1}\right)\). In the light of the above statements, choose the correct answer from the options given below

Statement\(-I :\) To get a steady de output from the pulsating voltage received from a full wave rectifier we can connect a capacitor across the output parallel to the load \({R}_{{L}}\) Statement\(-II :\) To get a steady de output from the pulsating voltage received from a full wave rectifier we can connect an inductor in series with \({R}_{{L}}\). In the light of the above statements, choose the most appropriate answer from the options given below:

A disc of mass \(1\,kg\) and radius \(R\) is free of rotate about a horizontal axis passing through its centre and perpendicular to the plane of disc. A body of same mass as that of disc is fixed at the highest point of the disc. Now the system is released, when the body comes to the lowest position, its angular speed will be \(4 \sqrt{\frac{x}{3 R}}\) rad s\(^{-1}\) where \(x=\) \(\left( g =10\,ms ^{-2}\right)\)

Identify the correct statements :
A. Effective capacitance of a series combination of capacitors is always smaller than the smallest capacitance of the capacitor in the combination.
B. When a dielectric medium is placed between the charged plates of a capacitor, displacement of charges cannot occur due to insulation property of dielectric.
C. Increasing of area of capacitor plate or decreasing of thickness of dielectric is an alternate method to increase the capacitance.
D. For a point charge, concentric spherical shells centered at the location of the charge are equipotential surfaces.
Choose the correct answer from the options given below.