Physics Test-7

The precision of a measuring tool is reflected in significant figures in the value.

Since 1 m = 1000 mm

As the given scale is a meter scale so it can measure 1000 mm with the least count of 1 mm.

The precision of any measuring tool depends on the size of its measurement increments.The smaller is the measurement increment, the more precise will be the tool.

The number having more digits after the points will be more precise because it can measure the very small differences in length. So option (C) is correct which is having 3 digits after the points.

The speed of revolving electron in \(n ^{\text {th }}\) state of hydrogen atom is

\(v =\frac{ e ^2}{2 nh \epsilon_0}\)

For \(n=1\)

\(v =\frac{\left(1.6 \times 10^{-19}\right)^2}{2(1)\left(6.6 \times 10^{-34}\right)\left(8.85 \times 10^{-12}\right)} \)

\(v =\frac{2.56 \times 10^{-38}}{116.82 \times 10^{-46}} \)

\(v =0.0219 \times 10^8 ~ ms ^{-1}\)

The speed of light is \(3 \times 10^8\)

So, \(\frac{ v }{ c }=\frac{0.0219 \times 10^8}{3 \times 10^8} \)

\(\frac{ v }{ c }=\frac{1}{137}\)

Ratio of rate of heat conduction to the rate of internal energy storage is in solid is known as Fourier number.

Fourier number is the ratio of heat conduction to the rate of heat storage. The significance of Fourier number is:

1. It signifies the degree of penetration of heating or cooling effect.

2. It is a measure of heat conducted through a body relative to heat stored.

If the particle moves in uniform circular motion of radius 'r', the period 'T' of its motion is \( \frac{2\pi}{\omega} \).

Glasses of the building appear milky because it undergoes heating during the day and cooling during the night. Therefore it acquires some crystalline properties.

If the frequency of the applied AC potential is increased in the R-L circuit, then the impedance of the circuit will increase.

We know that,

The reactance of the inductor coil is:

\(X_{L}=2 \pi f L\quad...(i)\)

And, the impedance of the R-L circuit is:

\(Z=\sqrt{R^{2}+X_{L}^{2}}\quad...(ii)\)

By equation \((i)\) and equation \((ii)\),

We get,

\(Z=\sqrt{R^{2}+(2 \pi f L)^{2}}\quad...(iii)\)

By equation \((iii)\) it is clear that if the frequency of the applied AC potential is increased in the R-L circuit, the impedance of the circuit will increase.

For any ‘AND GATE’ the three inputs are A, B and C then the output Y will beY = A . B . C.

The AND gate is a basic digital logic gate that implements logical conjunction \((∧)\) from mathematical logic – AND gate behaves according to the truth table above. A HIGH output \((1)\) results only if all the inputs to the AND gate are HIGH \((1)\). If none or not all inputs to the AND gate are HIGH, LOW output results.

First, draw the free body diagram of the given figure and resolve it into a horizontal and vertical component.

As we know that the value of the horizontal component is always zero irrespective of the inclination of the body.

So, the Horizontal component will be,

\(T_{1} \cos 30^{\circ}=100 \cos 60^{\circ} \)

\(\therefore T_{1}=\frac{100 }{ \sqrt{3}} N\)

Vertical Component will be,

\(T_{1} \sin 30^{\circ}+100 \sin 60^{\circ}= W\)

By putting the value of \(T_{1}\) from above we get

\(\frac{100}{\sqrt{3}} \times \frac{1}{2}+100 \times \frac{\sqrt{3}}{2}= W \)

\( \therefore W =\frac{200 }{ \sqrt{3}} N\)

Given that:

\(\phi=3 t^{2}+4 t+9\)

Number of turns is not given, so we will take is \(N=1\)

Time \((t)=2 \mathrm{sec}\)

We know that,

emf induced \((V)=-N \frac{d \varphi}{d t}\)

Where N is the number of turns, \(\phi\) is flux linked and t is time

Here negative sign shows the direction of the induced emf.

Now,

\((V)=-N \frac{d \varphi}{d t}\)

\(=-1 \times \frac{d\left(3 t^{2}+4 t+9\right)}{d t}\)

\(=-(6 t+4+0)\)

\(=-(6 t+4)\)

\(=-(6 \times 2+4)\)

\(=-16 V\)

Thus magnitude of emf induced \(=16V\)