Seema’s uncle was advised by his doctor to have an MRI (Magnetic Resonance Imaging) scan of his brain. Her uncle felt it to be expensive and wanted to postpone it.

When Seema learnt about this, she took the help of her family and also approached the doctor, who also offered a substantial discount. She then convinced her uncle to undergo the test to enable the doctor to know the condition of his brain. The information thus obtained greatly helped the doctor to treat him properly.

Based on the above paragraph, answer the following question:

(a) What according to you are the values displayed by Seema, her family and the doctor?

(b) What could be the possible reason for MRI test to be so expensive?

(c) Assuming that MRI test was performed using a magnetic field of 0.1T, find the minimum and maximum values of the force that the magnetic field could exert on a proton (charge= 1.6× 10^-19C) moving with a speed of 10⁴m/s.

(a) Derive the mathematical expression for law of radioactive decay for a sample of radioactive nucleus.

(b) How is the mean life of a given radioactive nucleus related to the decay constant?

(i) A screen is placed at a distance of 100 cm from an object. The image of the object is formed on the screen by a convex lens for two different locations of the lens separated by 20cm. calculate the focal length of the lens used.

(ii) A converging lens is kept coaxially in contact with a diverging lens- both the lenses being of equal focal length. What is the focal length of the combination?

(a) Distinguish, with a help of a suitable diagram, the difference in the behavior of a conductor and a dielectric placed in an external electric field. How does polarized dielectric modify the original external field?

(b) A capacitor of capacitance C is charged fully by connecting it to a battery of emf, E. it is then disconnected from the battery. If the separation between the plates of the capacitor is now doubled, how will the following change?

(i) charge stored by the capacitor.

(ii) field strength between the plates.

(iii) Energy stored by the capacitor.

Justify your answer in each case.

OR

(a) Explain why, for any charge configuration, the equipotential surface through a point is normal to the electric field at that point.

Draw a sketch of equipotential surfaces due to a single charge (-q), depicting the electric field lines due to the charge.

(b) Obtain an expression for the work done to dissociate the system of three charges placed at the vertices of an equilateral triangle of side ‘a’ as shown below.

(a) When a bar magnet is pushed towards (or away) from the coil connected to a galvanometer, the pointer in the galvanometer deflects. Identify the phenomenon causing this deflection and write the factors on which the amount and direction of the deflection depends. State the laws describing this phenomenon.

(b) Sketch the change in flux, emf and force when a conducting rod PQ of resistance R and length l moves freely to and fro between A and C with speed v on a rectangular conductor placed in uniform magnetic field as shown in figure.

OR

In a series LCR circuit connected to an a.c. source of voltage v= v_msinωt, use phasor diagram to derive an expression for the current in the circuit. Hence obtain the expression for the power dissipated in the circuit. Show that power dissipated at resonance is maximum.