Physics Test-14

Given:

Distance between the free protons, \(r=1\) Å\(=1 \times 10^{-10} \mathrm{~m}\)

Initially kinectic energy of the proton is zero and electric potential energy is maximum.

At infinite separation, potential energy is zero and all the energy is converted into kinetic energy (using law of conservation of energy)

i.e., \(2 \mathrm{~K}=\mathrm{U}\)

Where, \(K\) is kinetic energy of each proton.

\(K=\frac{1}{2} U=\frac{1}{2} \frac{e^{2}}{4 \pi \epsilon_{0} \mathrm{I}}\).....(1)

Where,

\(e=1.6 \times 10^{-19} \mathrm{C}\) (charge on the proton)

\(\epsilon_{0}=8.85 \times 10^{-12} \mathrm{C}^{2} \mathrm{~N}^{-1} \mathrm{~m}^{-2}\) (permittivity of free space)

Put all the given values in (1)

\(K=\frac{1}{2} \times \frac{\left(1.6 \times 10^{-19} \mathrm{C}\right)^{2}}{\left(10^{-10} \mathrm{~m}\right)} \times \frac{1}{4 \pi \epsilon_{0}} \)

\(\text { Also, } \frac{1}{4 \pi \epsilon_{0}}=9 \times 10^{9} \mathrm{Nm}^{2} \mathrm{C}^{-2} \)

\(\Rightarrow K=\frac{1}{2} \times \frac{\left(1.6 \times 10^{-19} \mathrm{C}\right)^{2}}{\left(10^{-10} \mathrm{~m}\right)} \times 9 \times 10^{9} \mathrm{Nm}^{2} \mathrm{C}^{-2} \)

\(\Rightarrow K=11.5 \times 10^{-19} \mathrm{~J}\)

Given:

\(v = 30 \) m/s, \(u = 10\) m/s, \(a = 4\) m/s^\(2\)

We know that,

\( v^{2}=u^{2}+2 a S\)

\(\Rightarrow 2 a S=v^{2}-u^{2}\)

\(\Rightarrow 2 \times 4 \times S=900-100\)

\(\Rightarrow 8 S=800\)

\(\Rightarrow S=\frac{800}{8}=100\) m

The displacement of the body is \(100\) m.

Given, M.I. of a thin uniform ring about an axis passing through the centre and perpendicular to plane is \(4 \mathrm{kgm}^{2}=\mathrm{mr}^{2}\)

Using Perpendicular axix theorem,

M.I. of a thin uniform ring about an axis passing through the centre and in the plane of the ring is \(2 \mathrm{kgm}^{2}=\) \(\frac{1}{2} \mathrm{mr}^{2}\)

Now, Using Parallel axix theorem,

M.I. of ring about an axis tangent to the ring and in a plane of the ring

\(\frac{1}{2} \mathrm{mr}^{2}+\mathrm{md}^{2}=\frac{3}{2} \mathrm{mr}^{2}\)

\(=\frac{3}{2} \mathrm{mr}^{2}=\left(\frac{3}{2}\right) 4 \mathrm{kgm}^{2}\)

\(=6 \mathrm{kgm}^{2}\)

Electrotypingdoes not involve chemical effect of electric current.

Electroplating: Electroplating (electro fabrication) is a chemical method for making metal parts that exactly reproduce a model. It is also done by electrolysis. Electroplating: Electroplating is the process of improving metals with a thin layer of a metal by electrolysis.

Here \(2 \Omega\) and \(2 \Omega\) are in parallel combination, therefore the resultant resistance is,

\(\Rightarrow \frac{1}{R_{p a r a}}=\frac{1}{2}+\frac{1}{6}=\frac{3+1}{6}=\frac{2}{3}\)

\(\Rightarrow\) Rpara \(=1.5 \Omega\)

Here \(1.5 \Omega\) and \(R_{\text {para }}\) are in series combination, therefore the resultant resistance is,

\(\Rightarrow R_{\text {ser }}=1.5 \Omega+1.5 \Omega=3 \Omega\)

Here \(3 \Omega\) and \(R_{\text {ser }}\) are in parallel combination, therefore the resultant resistance is,

\(\Rightarrow \frac{1}{R_{\text {net }}}=\frac{1}{3}+\frac{1}{3}=\frac{2}{3}\)

\(\Rightarrow R_{\text {net }}=1.5 \Omega\)

The current supplied by the battery in the circuit is given by,

\(\Rightarrow I=\frac{V}{R_{\text {net }}}=\frac{6}{1.5}=4 {~A}\)

According to the law of conservation of momentum, the total momentum of a system is conserved for an isolated system.

An isolated system means that there is no external interaction on the system.

Thus, the momentum of a system of particles is conserved if there is no external force acting on the system.

As we know,

\(\frac{1}{2} mv ^2= eV \)

\(mv =\sqrt{2 eV m } \)

And \( \lambda=\frac{ h }{ mV } \)

\(\frac{\lambda_0}{\lambda_1}=\frac{\sqrt{2 eV _1 m }}{\sqrt{ eV _2 m }} \)

\(\frac{\lambda_2}{\lambda_1}=\frac{1}{2} \)

\(\therefore \lambda_2=\frac{\lambda_1}{2} \)

\(R \propto \frac{1}{\lambda}\)

So, \(R\) would change to \(2 R\).

The unit of overall coefficient of heat transfer is kcal/m² hr °C.

kilocalorie per hour per square meter per degree Celsius (kcal/m² hr°С) is a metric unit of the heat transfer coefficient. The heat transfer coefficient has SI units in watts per squared meter kelvin: W/(m²K).