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Four particles having masses m, 2m, 3m and 4m are placed at the four corners of a square of edge a. Find the gravitational force acting on a particle of mass m placed at the centre.
A series $\text{LCR}$ circuit is connected to an $a.c$. source having voltage $V=V_m \sin \omega t$. Derive the expression for the instantaneous current $I$ and its phase relationship to the applied voltage. Obtain the condition for resonance to occur. Define power factor. State the conditions under which it is
$i.$ maximum and
$ii$. minimum.
State Soddy $-$ Fajan’s displacement laws for radioactive transformations.
Repeat the previous problem if the particle C is displaced through a distance x along the line AB.
Find the time period of the oscillation of mass $m$ in figure What is the equivalent spring constant of the pair of springs in each case?
Define common potential. Find the expression for redistribution of charges and energy loss when capacitors are connected together.
A bar magnet of length $1\ cm$ and cross-sectional area $1.0\ cm^2$ produces a magnetic field of $1.5 \times 10$. T at a point in end-on position at a distance $15\ cm$ away from the centre.
  1. Find the magnetic moment $M$ of the magnet.
  2. Find the magnetization $I$ of the magnet.
  3. Find the magnetic field $B$ at the centre of the magnet.
  1. Draw a ray diagram to show refraction of a ray of monochromatic light passing through a glass prism.
  1. Deduce the expression for the refractive index of glass in terms of angle of prism and angle of minimum deviation.
  2. Explain briefly how the phenomenon of total internal reflection is used in fibre optics.
A wave propagates on a string in the positive $x-$direction at a velocity v. The shape of the string at $t =$ to is given by $\text{g}(\text{x},\text{t}_0)=\text{A}\sin\big(\frac{\text{x}}{\text{a}}\big).$ Write the wave equation for a general time t.
A charge of $8 \ mC$ is located at the origin. Calculate the work done in taking a small charge of $–2 \times 10^{–9} C$ from a point $P (0, 0, 3 \ cm)$ to a point $Q (0, 4 \ cm, 0),$ via a point $R (0, 6 \ cm, 9 \ cm)$.