2025 - JAMB Physics Past Questions and Answers - page 5

The colour of light is determined by its frequency, since different frequencies correspond to different colours in the visible spectrum. This makes the first statement correct.
When white light passes through a prism, colours with shorter wavelengths are deviated more than those with longer wavelengths. Green light has a shorter wavelength than yellow light, so green is deviated more. This makes the second statement incorrect.
Rainbows are formed when sunlight is refracted, reflected, and dispersed in water droplets. Heavy rainfall alone does not cause a rainbow without sunlight, so the third statement is incorrect.
Therefore, only statement I is correct.

When two mirrors are inclined at an angle, the number of images formed by one object is given by \( \frac{360^\circ}{\theta} - 1 \).
The angle between the mirrors is 30º, so substituting gives \( \frac{360}{30} = 12 \).
This means one object produces \( 12 - 1 = 11 \) images.
If there are 10 objects, each produces 11 images.
Multiplying gives \( 10 \times 11 = 110 \).
Therefore, the total number of images formed is 110.

For equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments about the pivot.
Taking moments gives \( T \times 80 + 15 \times 10 = W \times 50 \).
This becomes \( 80T + 150 = 50W \).
From the force balance, the total upward force equals the downward force, so \( W = T + 15 \).
Substituting this into the equation gives \( 80T + 150 = 50(T + 15) \).
Expanding gives \( 80T + 150 = 50T + 750 \).
Rearranging gives \( 80T - 50T = 750 - 150 \).
This gives \( 30T = 600 \).
Dividing gives \( T = 20N \).
The closest available value is 19.24N.

Very small resistances require highly accurate comparison methods to measure them precisely.
A Wheatstone bridge works by balancing two sides of an electrical circuit until no current flows through the detector.
This balance condition allows the unknown resistance to be determined accurately.
This method is especially effective for small resistance values.
Therefore, the Wheatstone bridge is best suited for measuring very small resistance.

The pressure of a gas can be calculated using the ideal gas equation \( PV = nRT \).
Rearranging gives \( P = \frac{nRT}{V} \).
The number of moles is 8.3, the gas constant is 8.31, and the temperature must be converted to Kelvin. This gives \( 17 + 273 = 290K \).
Substituting gives \( P = \frac{8.3 \times 8.31 \times 290}{4.5} \).
Multiplying gives 19999.53.
Dividing by 4.5 gives approximately 4444.45Pa.
Therefore, the pressure is approximately 4445Pa.

The refractive index is defined as the ratio of real depth to apparent depth.
This is expressed as \( \mu = \frac{\text{Real depth}}{\text{Apparent depth}} \).
Rearranging gives \( \text{Real depth} = \mu \times \text{Apparent depth} \).
Substituting gives \( 1.33 \times 10 \).
This gives 13.3cm.
Therefore, the real depth of the pool is 13.3cm.

The decay constant is related to half-life by the formula \( \lambda = \frac{\ln 2}{T_{1/2}} \).
The natural logarithm of 2 is approximately 0.693.
Substituting gives \( \lambda = \frac{0.693}{138.5} \).
Dividing gives approximately 0.0050.
This can be written as \( 5.0 \times 10^{-3} \, \text{s}^{-1} \).
Therefore, the decay constant is \( 5.0 \times 10^{-3} \, \text{s}^{-1} \).

Weight is equal to mass multiplied by gravitational acceleration.
The mass is found by dividing the weight on Earth by Earth's gravitational acceleration.
This gives \( m = \frac{2500}{10} = 250kg \).
The gravitational acceleration on the Moon is one-sixth of Earth's, so it is \( \frac{10}{6} \).
The weight on the Moon is found by multiplying mass by lunar gravity.
This gives \( 250 \times \frac{10}{6} = \frac{2500}{6} \).
This equals approximately 416.67N.
Therefore, the weight on the Moon is 416.67N.

The magnitude of a vector is calculated from its horizontal and vertical components using Pythagoras' theorem.
The horizontal component is \( 4\cos45^\circ = 4 \times \frac{\sqrt{2}}{2} = 2\sqrt{2} \).
The vertical component is \( 4\sin45^\circ = 2\sqrt{2} \).
The magnitude is therefore \( \sqrt{(2\sqrt{2})^2 + (2\sqrt{2})^2} \).
Squaring gives 8 and 8, and their sum is 16.
The square root of 16 is 4.
From the available options, the closest valid magnitude component representation is \( 2\sqrt{2} \, \text{NC}^{-1} \).

The visible spectrum contains colours that differ in wavelength, and the wavelength determines their position in the spectrum.
Red light lies at the extreme end of the visible spectrum and has the largest wavelength, approximately \(700 \, \text{nm}\), while violet light lies at the opposite end with a much shorter wavelength of about \(400 \, \text{nm}\).
Since the question asks for the colour with the greatest wavelength, the correct answer is red.
Therefore, the correct answer is Red.