Physics Test-40

Surface tension is the property by virtue of which liquid tries to minimize its free surface area.

In a spherical shape, the surface area is minimum and for this reason, the raindrops are spherical.

Surface tension is measured as the force acting per unit length of an imaginary line drawn on the liquid surface.

\(\Rightarrow \frac{\text { Dyne}}{\text { cm}}\) or \(\text{Dyne}~\mathrm{cm}^{-1}\)

In nuclear physics, nuclear fusion is a nuclear reaction in which two or more atomic nuclei collide at a very high speed and join to form a new type of atomic nucleus. During this process, matter is not conserved because some of the matter of the fusing nuclei is converted to photons (energy).

Joining of light nuclei of elements to form a heavy nucleus with the release of energy is called nuclear fusion.

Stefan-Boltzmann law is applicable for radiation it states that the total radiant heat power emitted from a surface is proportional to the fourth power of its absolute temperature. The law applies only to black bodies, theoretical surfaces that absorb all incident heat radiation.

We know that the voltage sensitivity is given as,

\(V_{s}=\left(\frac{I_{s}}{R}\right) \quad \ldots\)(1)

Where, \(V _{ s }=\) voltage sensitivity, \(I _{ s }=\) current sensitivity, and \(R =\) resistance

When the resistance is increased by factor 2,

\(R^{\prime}=2 R\quad \ldots\)(2)

\(I_{s}^{\prime}=I_{s}+20 \% \text { of } I_{s}\)

\(\Rightarrow I_{s}^{\prime}=I_{s}+\frac{20}{100} I_{s}\)

\(\Rightarrow I_{s}^{\prime}=1.2 I_{s}\quad \ldots\)(3)

From equation (1) we get,

\( V_{s}^{\prime}=\frac{I_{s}^{\prime}}{R^{\prime}}\)

\(\Rightarrow V_{s}^{\prime}=\frac{1.2 I_{s}}{2 R}\quad \ldots\)(4)

By equation (1) and equation (4)

\(V_{s}^{\prime}=0.6 V_{s}\quad \ldots\)(5)

The change in voltage sensitivity is given as,

\(\% \Delta V=\frac{V_{s}^{\prime}-V_{s}}{V_{s}} \times 100\)

\(\Rightarrow \% \Delta V=\frac{0.6 V_{s}-V_{s}}{V_{s}} \times 100\)

\(\Rightarrow \% \Delta V=-40 \%\)

The formula for thecenterof mass of the two-particle systemis:

\(\Rightarrow r_{c m}=\frac{m_1 r_1+m_2 r_2}{m_1+m_2}\)

The insect can move on the surface of water due to the surface tension of water.

The weight of the insect and structure of their feet in combination with the surface tension of water allows some insects to walk on water.

Here the weight is balanced by the surface tension force.

We know that,

If there are two solenoids of equal length and one solenoid is placed coaxially inside the other solenoid then the mutual inductance of solenoid \(1\) with respect to solenoid \(2\) will be equal to the mutual inductance of solenoid \(2\) with respect to solenoid \(1\).

The mutual inductance of both the solenoids is given as,

\(M_{12}=M_{21}=\mu_{o} n_{1} n_{2} \pi r_{1}^{2} l\quad...(i)\)

Where \(n_{1}=\) number of turns per unit length of solenoid \(1, n_{2}=\) number of turns per unit length of solenoid \(2, r_{1}=\) radius of the inner solenoid, and \(I=\) length of both the solenoids

When the radius of the inner solenoid is halved, \(\left(r_{1}^{\prime}=\frac{r_{1}}{2}\right)\), the mutual inductance is given as,

\(M_{12}^{\prime}=M_{21}^{\prime}=\mu_{o} n_{1} n_{2} \pi\left(\frac{r_{1}}{2}\right)^{2} l\)

\(\Rightarrow M_{12}^{\prime}=M_{21}^{\prime}=\frac{\mu_{o} n_{1} n_{2} \pi r_{1}^{2} l}{4}\quad...(ii)\)

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

\(M_{12}^{\prime}=\frac{M_{12}}{4}\)

\(\Rightarrow M_{21}^{\prime}=\frac{M_{21}}{4}\)

\(p\)-type semiconductor is obtained by doping an intrinsic semiconductor with trivalent impurity.

The \(p\) stands for Positive, which means the semiconductor is rich in holes or Positive charged ions. When we dope intrinsic material with Pentavalent impurities we get \(n\)-Type semiconductor, where \(n\) stands for Negative.

Given, 

Radius \((r)=10 m\)

Velocity \((v)=10 m / s \)

\( g =10 m / s ^{2}\)

Free body diagram of the given condition,

So, \(F _{\text {net }}=0\)

\(T \sin \theta=\frac{m v^{2} }{ r} \)...(1) 

\(T \cos \theta=m g \)...(2) 

Dividing the equation (1) and (2), we get

\(\frac{T \sin \theta}{T \cos \theta}=\frac{v^{2}}{r g}\)

Substituting all the values in the above equation, we get

\(\frac{T \sin \theta}{T \cos \theta}=\frac{(10)^2}{10 \times 10} \)

\(\Rightarrow \frac{T \sin \theta}{T \cos \theta}=\frac{100}{100} \)

\(\Rightarrow \tan \theta=1\)

\(\Rightarrow \tan \theta=\tan 45^\circ\)

\(\therefore \theta= 45^\circ\)

The angle subtended by the rod from the path is \(45^{\circ}\).

The core of a transformer is laminated to reduce energy losses due to eddy currents.

In transformer, Due to Eddy current core is heated up so, energy loss. To reduced energy loss transformers are laminated. There are many causes due to which energy is lost in transformer. Eddy current is one of them. So as to minimize the lost heat by eddy currents, the core of transformer is laminated.