An isolated metal sphere of radius R, carrying an electric charge Q, is situated in the medium of relative permitivity, E^r. A test charge is placed at a point p, distance r from the surface of the sphere. Let E^o represent the permitivity of free space. The electric potential at p is given by the expression

• A. \(\frac{Q}{4 \pi E_o E_r}\)
• B. \(\frac{Q}{4 \pi E_o E_r (R +r)}\)
• C. \(\frac{Q}{4 \pi E_o E_r(R - r)}\)
• D. \(\frac{Q}{4 \pi E_o E_rR}\)

Which of the following quantities are dimensionally independent?

I. Dielectric constant II. Momentum III. Efficiency IV. Refractive index

• A. I and II
• B. II, III and IV
• C. I, II, III and IV
• D. I, III and IV

Under what conditions are cathode rays produced in a discharge tube?

• A. High pressure and low voltage
• B. High pressure and high voltage
• C. Low pressure and low voltage
• D. Low pressure and high volatge

Three cells each of emf, 1.0 V, and internal resistance, 2Ω, are connected in parallel across a 3Ω resistor. Determine the current in the resistor.

• A. 0.90A
• B. 0.39A
• C. 0.30A
• D. 0.01A

Which of the following eye defects can be corrected using a cylindrical lens.

• A. myopia
• B. Astigmatism
• C. Presbyopia
• D. Chromatic abiration

Calculate the angle of minimum deviation of a 60º prism of a refractive index 1.5[ sin^−1 (0.75) = 49º]

• A. 38^o
• B. 19.47^o
• C. 16.25^o
• D. 49^o

A light wave of frequency 5 x 10¹⁴Hz moves through water which has a refractive index of \(\frac{4}{3}\). Calculate the wavelength in water if the velocity of light in air is 3 x 10⁸ms^-1

• A. 4.5 x 10^-7m
• B. 6.0 x 10^-7m
• C. 1.7 x 10⁶m
• D. 2.2 x 10⁶m

When a resistor of resistance R is connected across a cell, the terminal p.d of the cell is reduced to three quarters of its e.m.f. The internal resistance of the cell is expressed as

• A. R/4
• B. R/3
• C. R/2
• D. 3R/4

Determine the focal length of a thin converging lens if the power is 5.0 dioptres

• A. 0.1 m
• B. 0.2 m
• C. 2.0 m
• D. 2.5 m

A 40KW electric cable was uses to transmit electricity through a resistor of resistance 2.00Ω at 800V. The power loss as internal energy is

• A) 4.0 x 10²W
• B) 5.0 x 10²W
• C) 4.0 x 10³W
• D) 5.0 x 10³W