Question
Taking an example of angular simple harmonic motion, establish an expression for the time period of the oscillator.

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A current i is passed through a silver strip of width d and area of cross-section A. The number of free electrons per unit volume is n.
  1. Find the drift velocity v of the electrons.
  2. If a magnetic field B exists in the region, as shown in the figure, what is the average magnetic force on the free electrons?
  3. Due to the magnetic force, the free electrons get accumulated on one side of the conductor along its length. This produces a transverse electric field in the conductor, which opposes the magnetic force on the electrons. Find the magnitude of the electric field which will stop further accumulation of electrons.
  4. What will be the potential difference developed across the width of the conductor due to the electron-accumulation? The appearance of a transverse emf, when a current-carrying wire is placed in a magnetic field, is called Hall effect.

Figure (a) shows a spring of force constant $k$ clamped rigidly at one end and a mass $m$ attached to its free end. A force $F$ applied at the free end stretches the spring. Figure (b) shows the same spring with both ends free and attached to a mass $m$ at either end. Each end of the spring in Fig. (b) is stretched by the same force $F$.
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(a) What is the maximum extension of the spring in the two cases?
(b) If the mass in Fig. (a) and the two masses in Fig. (b) are released, what is the period of oscillation in each case?
What is the excess pressure inside a bubble of soap solution of radius 5.00mm, given that the surface tension of soap solution at the temperature (20°C) is 2.50 × 10–2 Nm–1? If an air bubble of the same dimension were formed at depth of 40.0cm inside a container containing the soap solution (of relative density 1.20), what would be the pressure inside the bubble? (1 atmospheric pressure is 1.01 × 105Pa).
A uniform magnetic field B exists in a cylindrical region, shown dotted in figure. The magnetic field increases at a constant rate $\frac{\text{dB}}{\text{dt}}.$ Consider a circle of radius r coaxial with the cylindrical region.

  1. Find the magnitude of the electric field E at a point on the circumference of the circle.
  2. Consider a point P on the side of the square circumscribing the circle. Show that the component of the induced electric field at P along ba is the same as the magnitude found in part (a).


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Explain the angle of friction and angle of repose.
A capacitor of capacitance $2.0\mu\text{F}$ is charged to a potential difference of 12V. It is then connected to an uncharged capacitor of capacitance $4.0\mu\text{F}$ as shown in figure. Find:
  1. The charge on each of the two capacitors after the connection.
  2. The electrostatic energy stored in each of the two capacitors.
  3. The heat produced during the charge transfer from one capacitor to the other.

The blades of a windmill sweep out a circle of area A.
  1. If the wind flows at a velocity v perpendicular to the circle, what is the mass of the air passing through it in time t?
  2. What is the kinetic energy of the air?
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A pendulum clock gives correct time. What is the error in time per day if the length increases by 0.05%?