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10.15 Sound waves can propagate only through a medium. The two given situations are not scientifically identical because the motion of an observer relative to a medium is different in the two situations. Hence, the Doppler formulas for the two situations cannot be the same.

In case of light waves, sound can travel in a vacuum. In a vacuum, the above two cases are identical because the speed of light is independent of the motion of the observer and the notion of the source. When light travels in a medium, the above two cases are not identical because the speed of light depends on the wavelength of the medium.

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1.19 Net electric flux ( ${\phi }_{Net}$ ) through the cubic surface is given by

${\phi }_{Net}$ = $\frac{q}{{?}_0}$

where ${?}_0$ = Permittivity of free space = 8.854 ×${10}^{-12}$ $C^2{N}^{-1}$$m^{-2}$

q= 2.0 μC

${\phi }_{Net}$ =$\frac{2\times {10}^{-6}}{8.854\mathrm{}\times {10}^{-12}}$ $C^{-1}N$ $m^2=2.25\times {10}^5$ 

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10.14 The speed of light in vacuum (3 $*{10}^{8}m/s)$

is a universal constant. It is not affected by the motion of the source, the observer, or both. Hence, the given factor does not affect the speed of light in a vacuum.

Out of these 5 factors, the speed of light in a medium depends on the wavelength of light in that medium.

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• Marketing Manager
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10.13

Let an object at O be placed in front of a plane mirror MO' at a distance r. A circle is drawn from the centre (O) such that it just touches the plane mirror at point O'.

According to Huygens's principle, XY is the wave front of incident light.

If the mirror is absent, then a similar wave front X'Y' (as XY) would form behind O' at a distance r, as shown in the figure.

X'Y' can be considered as a virtual reflected ray for the plane mirror.

Hence, a point object placed in front of the plane mirror produces a virtual image whose distance from the mirror is equal to the object distance (r).

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MPT Orthopaedics graduates have strong career opportunities in both private and public sectors. They can work in hospitals, clinics, sports industries, and wellness centres.

Here's a table showing the main industries:

1.18 The square can be considered as one face of a cube of edge 10 cm with a centre where charge q is placed.

According to Gauss’s theorem for a cube, total electric flux is through all its six faces.

  ${\phi }_{Tota\mathrm{l\; =}}$$\frac{q}{{?}_0}$ 

$\mathrm{H}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e},\mathrm{}\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{}\mathrm{f}\mathrm{l}\mathrm{u}\mathrm{x}\mathrm{}\mathrm{t}\mathrm{h}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{g}\mathrm{h}\mathrm{}\mathrm{o}\mathrm{n}\mathrm{e}\mathrm{}\mathrm{f}\mathrm{a}\mathrm{c}\mathrm{e}\mathrm{}\mathrm{o}\mathrm{f}\mathrm{}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{}\mathrm{c}\mathrm{u}\mathrm{b}\mathrm{e}$ i.e. through the square is $\phi =\frac{{\phi }_{Total}}{6}$ = $\frac{q}{{6?}_0}$ ,Where${?}_0$= Permittivity of free space = 8.854
 $\times {10}^{-12}$ $C^2{N}^{-1}$$m^{-2}$

We have q = +10 $\mu C$

Hence,  = $\phi$ = $\frac{q}{{6?}_0}$ =$\frac{10\times {10}^{-6}}{6\times 8.854\mathrm{}\times {10}^{-12}}$= 188238.83 N$m^2{C}^{-1}$  = 1.88$\times {10}^5$ N$m^2{C}^{-1}$  

No, MPT Orthopaedics students cannot perform surgeries. They are trained to treat bone and joint problems through exercises, manual therapy, and rehabilitation.
Only licensed medical doctors (like MS Orthopaedics) are allowed to perform surgeries.
MPT graduates work closely with orthopaedic surgeons to support patients before and after surgical procedures.

10.11 The wavelength of $H_{?}$ line emitted by Hydrogen, $?=6563\AA$ = 6563 $*{10}^{-10}$ m$$

Star's red-shift, ( $?\text{'}$ $-$ $?)$ = 15 $\AA$ = 15 $*{10}^{-10}$ m

Speed of light, c = 3 $*{10}^8$ m/s

( $?\text{'}$ $-$ $?)$ = $\frac{v}{c}?$

v = $\frac{c}{?}*$ ( $?\text{'}$ $-$ $?)$ = $\frac{3\mathrm{}*{10}^8}{6563\mathrm{}*{10}^{-10}}*$ 15  $*{10}^{-10}$ = 6.86 $*{10}^5$ m/s

Yes, there is good demand for MPT Orthopaedics graduates. Hospitals, rehabilitation centres, sports clinics, and private practices often hire them.
Specialists in orthopaedic physiotherapy are needed to help patients recover after surgeries, injuries, or fractures.
With the rise in sports injuries and lifestyle-related bone problems, the demand is expected to grow even more in the future.

10.10 Fresnel's distance ( $Z_F)$ is the distance for which the ray optics is a good approximation. It is given by the relation

$Z_F=\frac{a^2}{?}$ where $a$ =aperture width = 4 mm = 4 $*{10}^{-3}$ m

$?$ = wave length = 400 nm = 400 $*{10}^{-9}$ m

Hence $Z_F=\frac{{4*{10}^{-3}}^2}{400\mathrm{}*{10}^{-9}}$ = 40 m

Therefore, the distance for which ray optics is a good approximation is 40 m.