List of practice Questions

A tank is filled with a liquid of refractive index \( \sqrt{2} \), up to a height of 30 cm. A tiny bulb is glowing at the bottom of the tank. Calculate the diameter of an opaque disc floating symmetrically on the liquid surface that can cut off completely the light from the bulb that comes out of the liquid surface.
An alpha particle and a deuterium ion are accelerated through the same potential difference. These are then directed towards a target nucleus to make a head-on collision. It is observed that their distance of closest approach is the same. Justify it theoretically.
A copper wire of uniform cross-sectional area carries a current of 3.4 A. The drift velocity of conduction electrons is 0.2 mm/s. If the number density of electrons in copper is \(8.5 \times 10^{28} \, \text{m}^{-3}\), find the area of cross-section of the wire.
A ray of light is incident on face AB of a prism ABC with angle of prism \( A \) and emerges out from face AC. The prism is set in the position of minimum deviation with angle of deviation \( \delta \). Find: \begin{enumerate} \item the angle of incidence and \item the angle of refraction on face AB. \end{enumerate}
Describe briefly the Geiger-Marsden scattering experiment. Depict the graph showing the variation of the number of scattered particles detected with the scattering angle. How did this graph lead to the discovery of the nucleus?
A conductor of length l and area of cross-section A is connected across an ideal battery of emf V . Derive the formula for the current density in terms of relaxation time τ
The ratio of potential difference across AB in the circuit shown for the case (i) when switch S is closed and (ii) when S is open is:
The ratio of potential difference across AB in the circuit
A laser beam of wavelength 500 nm and power 5 mW strikes normally on a perfectly reflecting surface of area 1 mm\(^2\) of a body. It rebounds back from the surface. Find the force exerted by the laser beam on the body.
A particle of mass \( m \) and charge \( q \) moving with velocity \( \vec{v} = v \hat{i} \) is subjected to a uniform electric field \( \vec{E} = E \hat{j} \). The particle will initially have a tendency to move in a circle of radius:
Define the term 'drift velocity' of conduction electrons in a conductor.
A ray of light is incident at an angle \( i \) on a parallel sided glass slab of thickness \( d \) and gets refracted into the slab at angle \( r \). Draw a ray diagram to show its path as it emerges out of the slab. Hence, obtain an expression for the lateral shift of the ray. Under what condition will the shift be minimum?
The de Broglie wavelength associated with an electron moving with energy 5 eV is:
An electric field \( \vec{E} = (10x + 5) \hat{i} \, \text{N/C} \) exists in a region in which a cube of side \( L \) is kept as shown in the figure. Here \( x \) and \( L \) are in metres. Calculate the net flux through the cube.
An electric field E⃗ = (10x + 5)ˆi N/C
A straight conductor is carrying a current of 2 A in the \( +x \) direction along it. A uniform magnetic field \( \vec{B} = (0.6 \hat{j} + 0.8 \hat{k}) \) T is switched on in the region. The force acting on 10 cm length of the conductor is:
A wire of resistance \( R \), connected to an ideal battery, consumes a power \( P \). If the wire is gradually stretched to double its initial length, and connected across the same battery, the power consumed will be:
A cell of emf \( E \) and internal resistance \( r \) is connected to an external variable resistance \( R \). Plot a graph showing the variation of terminal voltage \( V \) of the cell as a function of current \( I \), supplied by the cell. Explain how the emf of the cell and its internal resistance can be found from it.
The electric field in a region is given by \( \vec{E} = 40x \hat{i} \, \text{N/C}. \) Find the amount of work done in taking a unit positive charge from a point (0, 3m) to the point (5m, 0).
A charge \( Q \) is distributed over two concentric hollow spheres of radii \( r \) and \( R \) (\( R>r \)) such that their surface charge densities are equal. Find: \begin{enumerate} \item the electric field, and \item the potential at their common center. \end{enumerate}
A resistor of 400 \( \Omega \), an inductor of \( \frac{5}{\pi} \) H, and a capacitor of \( \frac{50}{\pi} \) µF are joined in series across an AC source \( v = 140 \sin (100 \pi t) \) V. Find the rms voltages across these three circuit elements. The algebraic sum of these voltages is more than the rms voltage of source. Explain.
Using Huygens’ principle, explain the refraction of a plane wavefront, propagating in air, at a plane interface between air and glass. Hence verify Snell’s law.
Use the mirror formula to deduce that a convex mirror always produces a virtual image of an object kept in front of it.
Draw a ray diagram to show the image formation by a compound microscope. Obtain the expression for the total magnification of the microscope when the final image is formed at infinity.
Write the principle of working of an ac generator. Draw its labelled diagram and explain its working.
Write the principle of working of a transformer. With the help of a labelled diagram, explain the working of a step-up transformer.

An ideal transformer is designed to convert 50 V into 250 V. It draws 200 W power from an AC source whose instantaneous voltage is given by \( v_i = 20 \sin(100\pi t) \, \text{V} \).

Find:

  • 1. RMS value of input current.
  • 2. Expression for instantaneous output voltage.
  • 3. Expression for instantaneous output current.