Physics Test-39

We know that:

Permittivity of free space is given by:

\(\epsilon_{0}=\frac{\mathrm{q}_{1} \mathrm{q}_{2}}{4 \pi \mathrm{Fr}^{2}}\)

Dimensions of \([\mathrm{F}]=\left[\mathrm{MLT}^{-2}\right]\)

Dimensions of \([\mathrm{q}]=[\mathrm{AT}]\)

Dimensions of \([\mathrm{r}]=[\mathrm{L}]\)

Thus, dimensional formula of \(\left[\epsilon_{0}\right]=\frac{[\mathrm{AT}][\mathrm{AT}]}{\left[\mathrm{MLT}^{-2}\right]\left[\mathrm{L}^{2}\right]}\)

\(\therefore \left[\epsilon_{0}\right]=\left[\mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{~T}^{4} \mathrm{~A}^{2}\right]\)

Magnetic compass connected in a circuit is used to check small current. LED glows when even a weak electric current flows through it. When a small amount of current is flowing through the conductor, the bulb will not glow as the filament of the bulb will not get heated up. Hence, in order to detect the presence of small value of current, we need magnetic compass. The magnetic compass will get deflected even if there is a small value of current.

It is observed that mass of a stable nucleus is always less than the total mass of constituent nucleons. This difference of mass is known as mass defect. When a nucleus is formed from the free nucleons mass defect is released in the form of energy by Einstein's mass-energy relation. This energy is used to bind the nucleons to form a nucleus therefore an equivalent amount of energy is required to split the nucleus into its parts, that is called the binding energy of the nucleus.

Maxwell’s 3rd equation is derived from Faraday’s laws of Electromagnetic Induction.

Maxwell's 3rd equation is given as:

\(\nabla \times E=-\frac{\partial B}{\partial t}\)

The negative sign indicates that the induced emf always opposes the time-varying magnetic flux. So, we can conclude that the time-varying magnetic field will always produce an electric field.

A quantity which can be measured and by which various physical phenomenon can be explained in the form of laws is called a physical quantity. For example length, mass, time, force etc.

Measurement is necessary to determine the magnitude of a physical quantity, to compare two similar physical quantities and to prove physical laws or equations.

Physical quantity \((Q)=\) Magnitude \(\times\) Unit \(=n \times u\)

Where \(\mathrm{n}\) represents the numerical value and u represents the unit.

n \(u=\) constant

\({n}_{1} {u}_{1}={n}_{2} {u}_{2}=\) constant

\(n \propto \frac{1}{u}\)

A battery is connected with a potentiometer wire. The internal resistance of the battery is negligible. If the length of the potentiometer wire of the same material and radius is doubled then potential gradient does not change.

Potential gradient Is given by \(\frac{V}{l}\). If V and l are constant, the potential gradient also remains constant. The change in the radius will cause a change in the current. This does not change the potential gradient.

Maximum velocity of the particle executing \({SHM}\) is given by \({v}={A w}\), where \(A\) is the amplitude and \(w=\sqrt{\frac{k}{m}}\)
Let the amplitude of the particle \(A\) and \(B\) be \(A_{1}\) and \(A_{2}\) respectively. Given: \({v}_{1}={v}_{2}\)
\({A}_{1} \times \sqrt{\frac{{k}_{1}}{{m}_{1}}}={A}_{2} \times \sqrt{\frac{{k}_{2}}{{m}_{2}}}\) \(\therefore {m}_{1}={m}_{2}\) \(\Rightarrow \frac{{A}_{1}}{{A}_{2}}=\sqrt{\frac{{k}_{2}}{{k}_{1}}}\)

\(\mathrm{G}\)is symbol used for gravitational constant, it is a universal constant and independent from type, place, mass, density, volume everything. It is always constant.

The value of universal gravitational constant\(\mathrm{(G})\)is$6.67\times {10}^{-11}{\mathrm{Nm}}^2/{\mathrm{Kg}}^2$,Which is constant and independent of mass, distance between the bodies, location, and other factors.

Kirchhoff’s second law is a consequence ofLaw of conservation of energy.

Work done in moving a charge in a closed circuit is zero, therefore the algebraic sum of potential differences in a closed circuit is zero.

A ball balanced on a vertical rod is an example of unstable equilibrium. A system is in unstable equilibrium if, when displaced from equilibrium, it experiences a net force or torque in the same direction as the displacement from equilibrium.

If a ball is placed on vertical rod, it is in unstable equilibrium because once it is displaced from its place, it will experience the net force in the direction of displacement and never come back to its original position. The potential energy of the ball is maximum at this point.