Physics Test-10

Given:

Electrostatic force of repulsion, \(F =3.7 \times 10^{-9} N\)

Let us say charge is \(q_{1}=q_{2}=q\)

Distance between two charges, \(r=5 \mathring A=5 \times 10^{-10} m\)

The number of electrons missing, \(n=\) ?

Using Coulomb's law,

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

\(3.7 \times 10^{-9}=9 \times 10^{9} \times \frac{ q \times q }{\left(5 \times 10^{-10^{2}}\right)^{2}}\)

\(q ^{2}=\frac{3.7 \times 10^{-9} \times 25 \times 10^{-20}}{9 \times 10^{9}}\)

\(q ^{2}=10.28 \times 10^{-38}\)

\(q=3.2 \times 10^{-19}\) Coulomb

As, we know that:

\(q=ne\)

\(\therefore n=\frac{q}{e}\)

\(=\frac{3.2 \times 10^{-19}}{1.6 \times 10^{-19}}\)

\(=2\)

Therefore, the number of electrons missing is \(n=2\).

An electrolyte is a substance that dissociates into ions in solution acquires the capacity to conduct electricity. Thus, electrolytic solutions contain only ions. So the charge carrier will be ion.

Since, velocity of a particle is 60% of the velocity of light.

Using reslativistic mass formula:

\(\mathrm{m}~=~\frac{\mathrm{m_o}}{\sqrt{1-\frac{\mathrm{v}^2}{\mathrm{c}^2}}}\)

where \(\mathrm{m_o}\) is rest mass of object, \(\mathrm{v}\) is velocity of the particle, \(\mathrm{c}\) is velocity of light.

\(\mathrm{m}~\)\(=~\frac{\mathrm{m_o}}{\sqrt{1- ~\frac{\left(\frac{60}{100} \mathrm{c}\right)^2}{\mathrm{C}^2}}} \quad(\because \mathrm{v}\) is \(60 \%\) of \(\mathrm{c})\)

\(\mathrm{m}~\)\(=~\frac{\mathrm{m_o}}{\sqrt{1-\frac{9}{25}}}\)

\(\mathrm{m}~\)\(=~\frac{\mathrm{m_o}}{\sqrt{\frac{16}{25}}}\)

\(\mathrm{m}~\)\(=~\frac{5 \mathrm{m_o}}{4}\)

So, \(\Delta \mathrm{m}~ = ~\frac{5}{4} \mathrm{m_o} - \mathrm{m_o} \) { \(\Delta \mathrm{m}\) = final value - initial value}

\(\Delta \mathrm{m}\) \( ~=\frac{\mathrm{m}_0}{4}\)

Overall percentage increase,\(=~\frac{\frac{\mathrm{m}_o }{ 4}}{\mathrm{~m}_o} \times 100\)

\(=~25 \%\)

Given Data:

Frequency \(=500 \mathrm{MHz}\)

Magnetic field \(\vec{B}=8.0 \times 10^{-8} \hat{z} T\)

Since the EM wave is always perpendicular to the magnetic field hence the EMwave is moving in the direction of \(\widehat{y}\) and light is an Electromagnetic wave.

Therefore, taking speed of light \(\vec{C}=3 \times 10^8 \hat{y} \mathrm{~ms}^{-1}\).

Calculating electric field,

\(\vec{E}=\vec{B} \times \vec{C}\)

\(\Rightarrow \vec{E}=\left(8 \times 10^{-8}\right) \hat{z} \times\left(3 \times 10^8\right) \hat{y}\)

\(\Rightarrow \vec{E}=-24 \hat{z} \hat{y}\)

\(\Rightarrow \vec{E}=-24 \hat{x} \frac{V}{m}\)

The fundamental units are the base units defined by International System of Units. These units are not derived from any other unit, therefore they are called fundamental units.The seven base units are:

• Meter (m) for Length
• Second (s) for Time
• Kilogram (kg) for Mass
• Ampere (A) for Electric current
• Kelvin (K) for temperature
• Mole (mol) for Amount of substance
• Candela (cd) for Luminous intensity

Voltis not a fundamental unit,it is a derived unit.

In a potentiometer experiment, for measuring internal resistance of a cell, the balance point has been obtained on the fourth wire. The balance point can be shifted to fifth wire by decreasing the current due to auxiliary battery

If the current due to the auxillary battery is decreased, the potential gradient will be decreases, so the balancing length increases.Thus null point will move to fifth wire.

In \(\mathrm{CH}_{3}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}_{3}\), there is more than one kind of hybridization are shown:

\({\underset{sp^3}{\underset{\downarrow}{\mathrm{CH}_{3}}}}-{\underset{sp^2}{\underset{\downarrow}{\mathrm{CH}}}}={\underset{sp^2}{\underset{\downarrow}{\mathrm{CH}}}}-{\underset{sp^3}{\underset{\downarrow}{\mathrm{CH_3}}}}\)

Kepler's law tells us that the square of the Time period (T) of a satellite is proportional to the cube of its distance (R) from the orbiting planet.

∴T²∝R³

The time period of earth's orbit around the sun is 1 year, and assuming the mean distance between earth and sun as R, we can write the mean distance between mars and the sun as 1.5R.

Let, T be the time period of mars' orbit around the sun.

Thus from the above proportionality,

$\frac{T^2}{R^3}$is a constant.

$\frac{{(1year)}^2}{R^3}=\frac{T^2}{{(1.5R)}^3}$

T² = (1.5)³

$T={(1.5)}^{\frac{3}{2}}$

≈1.85 years

Potentiometer measures the potential difference more accurately than a voltmeter, because the potentiometer does not draw current from external circuit.

On the other hand a voltmeter draws some current from the cell during measurement. When voltmeter is connected across the cell it amounts to closed circuit measurements and there is inner potential drop due to internal resistance of the cell. Therefore, the measurement of potential difference will not be accurate.

A roller coaster is an example of a non-uniform accelerated motion.

Acceleration: The increase in the velocity of a moving body with time is called acceleration.

There are two types of acceleration:

Uniform acceleration: The change in velocity is constant here. For example, if starting velocity is$5$m/s, next will be$10$m/s, then$15$m/s and so on.

Non-uniform acceleration: The change in velocity is not constant as in uniform acceleration.

The velocity of a roller coaster changes randomly and this is a perfect example of non-uniform accelerated motion.