Physics 2009 Jamb Examination

Secondary colours are formed by mixing two primary colours in equal proportions. The primary colours are red, blue, and green (in light). When red and green light mix, they produce yellow; green and blue produce cyan; and red and blue produce magenta. However, in pigments or paints, secondary colours are formed from red, yellow, and blue, giving orange, green, and purple. Therefore, orange is a secondary colour because it results from mixing red and yellow pigments.

When a positively charged rod is brought near the cap of an electroscope that already has a negative charge, it attracts some of the negative charges toward the cap, reducing the charge on the leaves. This decreases the repulsion between the leaves, causing them to close up. The redistribution of charges happens without contact, demonstrating electrostatic induction.

Power \( P = 60 \text{ W} \), and time \( t = 1 \text{ hour} = 3600 \text{ s} \).
The energy generated is given by \( E = P \times t \).\[E = 60 \times 3600 = 216000 \, \text{J}\]\[E = 2.16 \times 10^5 \text{ J}\]Therefore, the filament generates 2.16 × 10⁵ J of energy in one hour.

Number of loops, \( N = 500 \).
Area of one loop, \( A = 20 \text{ cm} \times 20 \text{ cm} = 0.2 \times 0.2 = 0.04 \text{ m}^2 \).
Change in magnetic field, \( \Delta B = 1.0 - 0.4 = 0.6 \text{ T} \).
Time interval, \( \Delta t = 5 \text{ s} \).
The induced e.m.f is given by Faraday’s law: \[E = \dfrac{N \Delta B A}{\Delta t}\]\[E = \dfrac{500 \times 0.6 \times 0.04}{5} = \dfrac{12}{5} = 2.4 \text{ V}\]Hence, the induced e.m.f. is 2.40 V.

Natural sources of light are those that emit light without human intervention. The Sun and stars produce their own light naturally through nuclear reactions, while the Moon only reflects light from the Sun and street lights are artificial. Therefore, only the Sun (II) and stars (IV) are natural sources of light.

Given \( f = 10 \text{ cm} \) and \( u = 5 \text{ cm} \) (object distance, negative by convention for mirrors).
Mirror formula: \[\dfrac{1}{f} = \dfrac{1}{u} + \dfrac{1}{v}\]\[\dfrac{1}{10} = \dfrac{1}{-5} + \dfrac{1}{v}\]\[\dfrac{1}{v} = \dfrac{1}{10} + \dfrac{1}{5} = \dfrac{3}{10}\]\[v = \dfrac{10}{3} = 3.33 \text{ cm}\]Since the image forms behind the mirror, it is virtual and the correct position is 10 cm behind the mirror.

For a convex mirror, focal length \( f = +12 \text{ cm} \), image distance \( v = -6 \text{ cm} \) (since image is virtual).
Using mirror formula: \[\dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u}\]\[\dfrac{1}{12} = \dfrac{1}{-6} + \dfrac{1}{u}\]\[\dfrac{1}{u} = \dfrac{1}{12} + \dfrac{1}{6} = \dfrac{3}{12} = \dfrac{1}{4}\]\[u = 4 \text{ cm}\]Therefore, the object is placed 4.0 cm in front of the mirror.

The critical angle \( C \) is given by \( \sin C = \dfrac{1}{n} \), where \( n \) is the refractive index of the medium.\[\sin C = \dfrac{1}{1.51} = 0.662\]\[C = \sin^{-1}(0.662) = 41.5^\circ\]Hence, the critical angle for crown glass is approximately 41.5°.

The speed of light in a medium is given by \( v = \dfrac{c}{n} \), where \( n \) is the refractive index. A higher refractive index means light travels slower. Since medium x has \( n = 1.51 \) and medium y has \( n = 1.33 \), light travels slower in x and faster in y. Therefore, the speed of light in y is higher than in x.

When two bodies coalesce after collision, the principle of conservation of momentum applies.
Let the common velocity be \(v\).
Initial momentum = final momentum.\[m_1u_1 + m_2u_2 = (m_1 + m_2)v\]\[12 \times 4.2 + 18 \times 0 = (12 + 18)v\]\[50.4 = 30v\]\[v = \dfrac{50.4}{30} = 1.68 \text{ ms}^{-1}\]Therefore, the common velocity is approximately 1.7 ms^-1.