\(sin\theta =\theta \)
\(\tau =mB\quad sin\theta =mB\theta \)
This torque is in the nature of a restoring torque.
Hence equation of motion, for the oscillatory motion, of the magnet is
\(I\frac { { d }^{ 2 }\theta }{ dt^{ 2 } } =-mB\theta \)
This is the equation of a S.H.M.
\(\frac { { d }^{ 2 }\theta }{ dt^{ 2 } } +\omega ^{ 2 }\theta =0\)
where  \({ \omega }^{ 2 }=\frac { mB }{ I } \)
Hence the time period of oscillation of the magnet is given by
\(T=\frac { 2\pi }{ \omega } \)
\(=2\pi \sqrt { \frac { I }{ mB } } \)

m_net = 2m
I_net = 2I
\(\Rightarrow \) T will remain same.

(i) Here,
\(\lambda =600 \ nm=600\times { 10 }^{ -9 }m=6\times { 10 }^{ -7 }m\)
\(\theta ={ 0.1 }^{ \circ }=\frac { 0.1\pi }{ 180 } rad,d=?\)
From angular width,\(\theta =\frac { \lambda }{ d } \)
\(\Rightarrow \ d=\frac { \lambda }{ \theta } =\frac { 6\times { 10 }^{ -7 } }{ \frac { \pi }{ 180 } \times 0.1 } =3.44\times { 10 }^{ -4 }m\)
(ii) The frequency and wavelength of reflected wave will not change. The refracted wave will have same frequency. The velocity of light in water is given by \(v=f\lambda \)
where, v = velocity of light
f = frequency of light
​​​​​​​​​​​​\( ​​lambda =wavelength \ of \ light\)
If velocity will decrease, then wavelength (\(\lambda \)) will also decrease.

(i) The values shown by him are as follows:
(a) Consulting others in case of need
(b) Curosity
(c) Sharing knowledge.
(ii) From these three lenses, he will use a lens of power 0.5D for objective and lens of power 10D for eyepiece.

(i) The device that is used to bring high voltage down to low voltage of an AC current is a transformer. It works on the principle of mutual induction of two windings or circuits. When current in one circuit changes, emf is induced in the neighbouring circuit.
(ii) The transformer cannot convert DC voltages because it works on the principle of mutual induction. When the current linked with the primary coil changes, the magnetic flux linked with secondary coil also changes. This change in flux induces emf in the secondary coil. If we apply a direct current to the primary coil, then current will remain constant. Thus there is no mutual induction, and hence, no emf is induced.
(iii) The value of gaining knowledge and curiosity about learning new things is being displayed by the students. The value of providing good education and undertaking the doubts of students has been displayed by teacher.

i) The values developed by Mndeep were sympathy, responsibility, helping nature and self-reliance.
ii) The vlue imparted by mother are appreciation and thankfulness.
iii) It is not necessary that every magnetic configuration has a North pole and a South pole.It is true only if the source of the field has a net non-zero magnetic moment.This is not possible for a toroid or even for a straight infinite conductor.

Applied voltage, V = 140 \(sin\ 100\pi t\ V\)
\(C \ = \ \frac { 50 }{ \pi } \mu F=\frac { 50 }{ \pi } \times { 10 }^{ -6 }F.\\ L \ = \ \frac { 5 }{ \pi } H, \ R=400\Omega \)
Comparing with V = V₀ \(sin\ \omega t,\) we get
V₀ = 140 V and \(\omega =100\pi \)
Inducting reactance, 
\({ X }_{ L }=\omega L=100\pi \times \frac { 5 }{ \pi } =500\Omega \)
Capacitive reactance,
\({ X }_{ C }=\frac { 1 }{ \omega C } =\frac { 1 }{ 100\pi \times \frac { 50 }{ \pi } \times { 10 }^{ -6 } } \)
\(=200\Omega \quad \)
Impedance of the circuit, 
\(Z=\sqrt { { R }^{ 2 }+({ X }_{ L }-{ X }_{ C })^{ 2 } } \)
\(=\sqrt { ({ 400) }^{ 2 }+({ 500-200) }^{ 2 } } \)
\( =\sqrt { 1600+900 } \ = \ 500\Omega \)
Maximum current in the circuit,
\({ I }_{ 0 }=\frac { { V }_{ 0 } }{ Z } =\frac { 140 }{ 500 }\)
\( { I }_{ rms }=\frac { { I }_{ 0 } }{ \sqrt { 2 } } =\frac { 140 }{ 500\times \sqrt { 2 } } =0.2\quad A\)
\({ V }_{ rms }\) across resistor, V_R = I_rms R
\(=0.2\times 400\ =\ 80V\)
Vrms across capacitor, V_C = I_rms X_L
\(=0.2\times 200\ =\ 40V\)
Now,   \(V\neq { V }_{ R }+{ V }_{ L }+{ V }_{ C }\)
Because V_C,V_L and V_R are not in same phase, instead
 \(V=\sqrt { { V }_{ R }^{ 2 }+({ V }_{ L }-{ V }_{ C })^{ 2 } } \)
\(=\sqrt { { 80 }^{ 2 }+({ 100-40) }^{ 2 } } =100V\)
Which is same as that of applied rms voltage.

According to Brewster's law,
\(\mu =tanp....(i)\)
\(Also \ \mu =\frac { 1 }{ sin\quad C } .....(ii)\)
\( From \ (i) \ and \ (ii), \ tanp=\frac { 1 }{ sin \ C } \)
\(If \ r \ is \ angle \ of \ refraction, \ then \ p=90°-r\)
\(or \ tan \ r=sin \ C \ r={ tan }^{ -1 }(sin \ C)\)