Physics Test - 23

Given masses of three liquids are equal,

i.e. \(m_x=m_y=m_z=m\)

Temperature of mixture of liquids \(x\) and \(y, \mathrm{~T}_1=16^{\circ} \mathrm{C}\)

Temperature of mixture of liquids \(y\) and \(z, T_2=26^{\circ} \mathrm{C}\)

While mixing the liquids \(x\) and \(y\), the heat energy lost by liquid \(y\)

will be equal to the heat energy absorbed by liquid \(x\).

Consider the specific heat capacity of liquid \(\mathrm{x}\) is \(s_x\), of liquid \(\mathrm{y}\) is \(s_y\)

and of liquid \(\mathrm{z}\) is \(s_z\).

Now, for liquid \(\mathrm{x}\) and \(\mathrm{y}\), using principle of calorimetry,

Heat gained by liquid \(x=\) Heat lost by liquid \(y\)

\(m s_x\left(\mathrm{~T}_1-10\right)=m s_y\left(20-\mathrm{T}_1\right) \)

\(\Rightarrow s_x(16-10)=s_y(20-16) \)

\(\Rightarrow \frac{s_x}{s_y}=\frac{2}{3} \ldots(\mathrm{i})\)

Similarly, for liquid \(y\) and \(z\), using principle of calorimetry,

Heat gained by liquid \(\mathrm{y}=\) Heat lost by liquid \(\mathrm{z}\)

\(m s_y\left(\mathrm{~T}_2-20\right)=m s_z\left(30-\mathrm{T}_2\right) \)

\(\Rightarrow s_y(26-20)=s_z(30-26) \ldots \)

\(\Rightarrow \frac{s_y}{s_z}=\frac{2}{3} \ldots \text { (i) }\)

Multiply Eq. (i) by Eq. (ii), we get

\(\frac{s_x}{s_z}=\frac{4}{9}\)

Consider the mixing of liquids \(x\) and \(z\), let the temperature of mixture be \(T_3\).

Using principle of calorimetry for liquids \(x\) and \(z\).

Heat gained by liquid \(x=\) Heat lost by liquid \(z\)

\(m s_x\left(\mathrm{~T}_3-10\right)=m_z\left(30-\mathrm{T}_3\right)\)

\(\Rightarrow s_x\left(\mathrm{~T}_3-10\right)=s_z\left(30-\mathrm{T}_3\right)\)

\(\Rightarrow \frac{s_x}{s_z}=\frac{30-\mathrm{T}_3}{\mathrm{~T}_3-10} \)

\(\Rightarrow \frac{4}{9}=\frac{30-\mathrm{T}_3}{\mathrm{~T}_3-10} \)

\(\Rightarrow 4 \mathrm{~T}_3-40=270-9 \mathrm{~T}_3 \)

\(\Rightarrow \mathrm{T}_3=23.84^{\circ} \mathrm{C}\)

Electromagnetic waves are the transverse waves.

Transverse Waves:

• Those waves whose direction of propagation and direction of disturbance is always perpendicular, are known as transverse waves.
• These waves produced in a medium that can sustain shearing strain.
• Example: Electromagnetic Waves, Ripples on the surface of water, Vibrations in a guitar string.

Given:

\(\theta=60^{\circ},E=10^{5}NC^{-1},T=8\sqrt{3}Nm\)

Electric field strength \(=\mathrm{E}=[\frac{\mathrm{T}}{(\mathrm{P} \sin \theta)}]\)

Where \(\mathrm{P}\) is dipole moment

\(\therefore 10^{5}=[\frac{(8 \sqrt{3})}{(\mathrm{P} \sin 60^{\circ})}]\)

\(\therefore \mathrm{P}=\left[\frac{(8 \sqrt{3})} {\left\{(\frac{\sqrt{3} }{ 2}) \times 10^{5}\right\}}\right]=16 \times 10^{-5} \mathrm{c}-\mathrm{m}\)

As \(P=q \cdot(2 \ell)\)

Here \(2 \ell=\) length of dipole \(=2 \times 10^{-2} \mathrm{~m}\)

\(\therefore q=(\frac{P} { 2 \ell})\)

\(=\left[\frac{\left(16 \times 10^{-5}\right)} {\left(2 \times 10^{-2}\right)}\right]=8 \times 10^{-3} \mathrm{c}\)

Self-induction in a coil measures the size of electromotive force or voltage induced in the coil. If the electromotive force in a conductor differs from the one in which the current is changing, then we say this phenomenon is mutual induction. Also, the changing magnetic field occurring due to the varying current in the conductor induces the varying current in the conductor. We call this phenomenon self-inductance. It also opposes the change to bring it about.

Now, when a current starts to flow through the coil of wire then the flow of current is opposed by the resistance of the metal of the wire. Then it is obvious that the self-inductance will come into play and it works as electromagnetic inertia that opposes the change in the electric current and the change in the magnetic field of the system. From the above statements, we came to know that the self-inductance of the coil is used to measure the electrical inertial.

Given that:

Separation distance, \(r=5.12 \times 10^{-15} \) m

We know that:

Charge on an electron, \(e=1.6 \times 10^{-19}\)

and, \(\frac{1}{4 \pi \epsilon_{0}}=9 \times 10^{9}\)

Charge on an alpha particle is \(2 e\).

\(\therefore\) Using Coulomb's law,

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

\(=\frac{1}{4 \pi \epsilon_{0}} \frac{2 \times 1.6 \times 10^{-19} \times 1.6 \times 10^{-19}}{\left(5.12 \times 10^{-15}\right)^{2}} \)

\(=9 \times 10^{9} \times 0.195 \times 10^{-8} \)

\(=17.5 \) N

The length of a simple pendulum is increased then the time period will increase.

• For a simple pendulum, the time period of swing of a pendulum depends on the length of the string and acceleration due to gravity.

\(\Rightarrow T=2 \pi \sqrt{\frac{l}{g}}\)

• From the above equation, it is clear that the period of oscillation is directly proportional to the length of the arm and inversely proportional to acceleration due to gravity.
• Thus, an increase in the length of a pendulum arm results in a subsequent increase in the period of oscillation given a constant gravitational acceleration.

The centre of mass is closer to a massive part of the body, therefore, the bottom piece of the bat has a larger mass.

For correcting myopia, a concave lens is used and for the lens.

\(\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\)

\(\Rightarrow \frac{1}{f}=\frac{1}{-25}-\frac{1}{(-50)}\)

\(\Rightarrow f=-50 \mathrm{~cm} \quad\)

So power,

\(P=\frac{100}{f}\)

\(=\frac{100}{-50}\)

\(=-2 \mathrm{D}\)

The Reflected ray of light, when the angle of incidence is Brewster angle, would comprise of only the other component of light wave which is oscillating in a direction perpendicular to vibration of electric field vectors.