Physics

The period T is the time taken to complete one full revolution (2? radians). In uniform circular motion, it relates to angular velocity by? =2? /T and to tangential speed by v=? r=2? r/T .

Using equation of continuity

$\begin{array}{rr}& A_1{V}_1=A_2{V}_2\\ & \frac{V_1}{V_2}=\frac{A_2}{A_1}={\left(\frac{d_2}{d_1}\right)}^2={\left(\frac{4.8}{6.4}\right)}^2=\frac{9}{16}\end{array}$

$A=A_0{e}^{-\lambda t}$

$\begin{array}{rr}& 500=700{\mathrm{e}}^{-\lambda \mathrm{t}}\\ & \lambda \mathrm{t}=\mathrm{l}\mathrm{n}?\frac{7}{5}\\ & \frac{\mathrm{l}\mathrm{n}?2}{{\mathrm{t}}_{1/2}}*30=\mathrm{l}\mathrm{n}?\frac{7}{5}\\ & ?\mathrm{}{\mathrm{t}}_{1/2}=\frac{\mathrm{l}\mathrm{n}?2*30}{\mathrm{l}\mathrm{n}?\frac{7}{5}}\end{array}$

${\mathrm{t}}_{1/2}=61.8\mathrm{m}\mathrm{i}\mathrm{n}\approx 62\mathrm{m}\mathrm{i}\mathrm{n}$

$x=$ retentivity

$y=$ coercivity

$\mathrm{z}=$ saturation magnetization

$\frac{\text{Energy}}{\text{Volume}}=\frac{{\mathrm{M}\mathrm{L}}^2{\mathrm{T}}^{-2}}{{\mathrm{L}}^3}=\left({\mathrm{M}\mathrm{L}}^{-1}{\mathrm{T}}^{-2}\right)$

 The distance between two successive bright fringes is fringe width $\left(\beta \right)$ .

$\beta =\frac{\lambda D}{d}=\frac{589*{10}^{-9}*1.5}{0.15*{10}^{-3}}=5.9\mathrm{m}\mathrm{m}$

Magnetic energy per unit volume $=\frac{{\mathrm{B}}^2}{2{?}_0}$

$\mathrm{}{W}_{\text{equator}}=W_{\text{pole}}-m{\omega }^{2}R$

$\begin{array}{rr}& =196-19.6*{\left(\frac{2\pi }{24*60*60}\right)}^2*6400*{10}^3\\ & =195.33\mathrm{N}\end{array}$

The principle of circular motion follows Newtonian mechanics. It can be stated that an object will move in a circle only when there is a centripetal force that continuously acts perpendicular to its tangential velocity. That changes the direction but not its speed. The inward acceleration a_c = v squared/r obeys Newton's laws and ensures circular path motion. 

Circular motion has the following characteristics.

• Fixed radius with the same and constant distance from the centre
• Constant speed, when the motion is uniform
• A changing velocity vector with continuous direction of change
• Centripetal acceleration that is directed radially inwards, while the force that causes it is the centripetal force that maintains the curved path

$\mathrm{W}={\mathrm{Q}}_1-{\mathrm{Q}}_2={\mathrm{Q}}_2-{\mathrm{Q}}_3$

${\mathrm{Q}}_2=\frac{{\mathrm{Q}}_1+{\mathrm{Q}}_3}{2}$

$2=\frac{{\mathrm{Q}}_1}{{\mathrm{Q}}_2}+\frac{{\mathrm{Q}}_3}{{\mathrm{Q}}_2}$

$2=\frac{T_1}{T}+\frac{T_2}{T}$

$\mathrm{T}=\frac{{\mathrm{T}}_1+{\mathrm{T}}_2}{2}$