## Important 5 marks Questions – Physics – Class 12

**Question 1**

(a) Define electric dipole moment. Derive the expression for the electric field of a dipole at a point on the equatorial plane of the dipole. Is it a scalar or a vector?

(b) Draw the equipotential surfaces due to an electric dipole. Locate the points where the potential due to the dipole is zero.

**Question 2**

- Using Biot-Savart’s law, derive the expression for the magnetic field in the vector form at a point on the axis of a circular current loop.
- What does a toroid consist of? Find out the expression for the magnetic field inside a toroid for N turns of the coil having the average radius r and carrying a current I. Show that the magnetic field in the open space inside the exterior of the toroid is zero.

**Question 3**

Using Bohr’s postulates, derive the expression for the frequency of radiation emitted when an electron in a hydrogen atom undergoes the transition from a higher energy state quantum number n_{i}) to the lower state (n_{f}). When electron in hydrogen jumps from energy state n_{i} = 4 to n_{r} = 3,2,1, identify the spectral series to which the emission lines belong.

**Question 4**

Using Gauss’ law, deduce the expression for the electric field due to a uniformly charged spherical conducting shell of radius R at a point.

(i) Outside

(ii) Inside the shell.

Plot a graph showing the variation of the electric field as a function of r > R and r < R (r is the distance from the centre of a shell)

**Question 5**

- Draw the plot of binding energy per nucleon (BE/A) as a function of mass number A. Write two important conclusions that can be drawn regarding the nature of nuclear force.
- Use this graph to explain the release of energy in both the process of nuclear fusion and fission.
- Write the basic nuclear process of neutron undergoing β -decay. Why is the detection of neutrinos found very difficult?

**Question 6**

- Draw a schematic sketch of a cyclotron. Explain clearly the role of the crossed electric and magnetic fields in accelerating the charge. Hence, derive the expression for the kinetic energy acquired by the particles.
- An α-particle and a proton are released from the centre of the cyclotron and made to accelerate.

(i) Can both be accelerated at the same cyclotron frequency? Give the reason to justify your answer.

(ii) When they are accelerated in turn, which of the two will have a higher velocity at the exit slit of the dees?

**Question 7**

Draw a labelled diagram of the Van de Graaff generator. State its working principle to show how a large amount of charge can be transferred to the outer sphere by introducing a small charged sphere into a larger sphere. State the use of this machine and also point out its limitations.

**Question 8**

- Deduce the expression for the torque acting on a dipole moment p in the presence of a uniform electric field \(\begin{array}{l}\vec{E}\end{array} \)
- Consider two hollow concentric spheres S
_{1}and S_{2}enclosing charges 2Q and 4Q respectively. Thus find the ratio of the electric flux through them. Also, tell how will the electric flux through the sphere S_{1}change if a medium of dielectric constant ‘L’ is introduced into the space inside S_{1}in place of air?

Deduce the necessary expression.

**Question 9**

- In Young’s double-slit experiment, describe briefly how bright and dark fringes are obtained on the screen kept in front of a double slit. Hence, obtain the expression for the fringe width.
- The ratio of the intensities at minima to the maxima in Young’s double-slit experiment is 9:25. Then find the ratio of the widths of the two slits.

**Question 10**

- Describe briefly how a diffraction pattern is obtained on a screen due to a single narrow slit illuminated by a monochromatic source of light. Hence, obtain the conditions for the angular width of secondary maxima and secondary minima.
- Two wavelengths of sodium light of 590 nm and 596 nm are used in turn to study the diffraction taking place at a single slit of aperture 2 x 10
^{-8}m. The distance between the slit and the screen is 1.5 m. Calculate the separation between the position of the first maxima of the diffraction pattern obtained in the two cases.

**Question 11**

- Draw a labelled diagram of a moving coil galvanometer. Briefly describe its principle and functioning.
- Answer the following-

(i) Why is it necessary to introduce a cylindrical soft iron core inside the coil of a galvanometer?

(ii) Increasing the current sensitivity of a galvanometer may not necessarily increase its voltage sensitivity. Explain, giving a reason.

**Question 12**

- Deduce an expression for the frequency of revolution of a charged particle in a magnetic field and show that it is independent of the energy of the particle.
- Draw a schematic sketch of a cyclotron. Explain, giving the essential details of its construction, and how it is used to accelerate the charged particles.

**Question 13**

- Define wavefront. Use Huygens’ principle to verify the laws of refraction.
- How is linearly polarized light obtained by the process of scattering of light? Find the Brewster angle for an air-glass interface when the refractive index of glass = 1.5.

**Question 14**

- Draw a ray diagram to show the image formation by a combination of two thin convex lenses in contact. Obtain the expression for the power of these terms of the focal lengths of the lenses.
- A ray of light passing from the air through an equilateral glass prism undergoes minimum deviation when the angle of incidence is 3/4th of the angle of prism. Calculate the speed of light in the prism.

**Question 15**

A police jeep moving with a velocity of 45 kmph is chasing a thief who in another jeep is moving with a velocity of 153 kmph. A policeman fires a bullet with a muzzle velocity of 180 m/s. What is the velocity with which it will strike the thief’s car?

**Question 16**

Derive an expression for the loss in KE in a completely inelastic collision in one dimension.

**Question 17**

The driver of an automobile moving with a speed of 36kmph sees a child standing in the middle of a road and brings his vehicle to rest in 4s to save the child. The automobile’s mass is 1200 kg, and the driver’s mass is 50 kg. What is the average retarding force on the vehicle?

**Question 18**

State the work-energy theorem. Prove it.

**Question 19**

Obtain the expression for acceleration due to gravity at a height “h” above the earth’s surface.