2025 - JAMB Physics Past Questions and Answers - page 7

In a pinhole camera, the relationship between image size, object size, image distance, and object distance follows the magnification relation
\[\text{Magnification} = \frac{\text{Image size}}{\text{Object size}} = \frac{v}{u}\]
where \(v\) is the distance from the pinhole to the image (camera length) and \(u\) is the object distance.
The camera length is given as 25 cm, which is equal to 0.25 m.
The image is one-fifth the size of the object, so the magnification is
\[\frac{1}{5} = \frac{v}{u}\]
Substituting the value of \(v\),
\[\frac{1}{5} = \frac{0.25}{u}\]
Multiplying both sides by \(u\),
\[u \times \frac{1}{5} = 0.25\]
Multiplying both sides by 5 gives
\[u = 0.25 \times 5\]
\[u = 1.25 \, \text{m}\]
Therefore, the object distance is 1.25 m.

The force required to lift the mass is equal to its weight because a fixed pulley only changes the direction of the force without reducing its magnitude.
The weight is calculated using
\[F = mg\]
Substituting the given values,
\[F = 20 \times 10 = 200 \, \text{N}\]
Power is defined as the rate of doing work and can be calculated using the relation
\[P = Fv\]
Substituting the values,
\[P = 200 \times 5\]
\[P = 1000 \, \text{W}\]
Therefore, the power developed by the boy is 1000 W.

When a string is plucked, the particles of the string move perpendicular to the direction in which the wave travels.
This type of motion is called transverse motion, and therefore the wave produced is a transverse wave.
Such waves are mechanical because they require a material medium to travel through, and they also have crests and troughs.
A longitudinal wave, however, involves motion parallel to the direction of wave travel, which does not occur in a plucked string.
Therefore, the incorrect statement is that the wave is longitudinal.

The first displacement is 6.0 m towards the East.
The second displacement is 10.0 m at an angle of 30º East of North. This means the angle between the East direction and the N30ºE direction is 60º.
The resultant displacement can be found using the cosine rule
\[R^2 = a^2 + b^2 + 2ab\cos\theta\]
Substituting the values,
\[R^2 = 6^2 + 10^2 + 2(6)(10)\cos60^\circ\]
Since \(\cos60^\circ = 0.5\),
\[R^2 = 36 + 100 + 120(0.5)\]
\[R^2 = 36 + 100 + 60\]
\[R^2 = 196\]
Taking the square root,
\[R = \sqrt{196} = 14.0 \, \text{m}\]
Therefore, his distance from the starting point is 14.0 m.

When a substance changes from solid to liquid without a change in temperature, the heat supplied is used to overcome intermolecular forces rather than increase temperature.
This type of heat is called latent heat.
Since the change involved is from solid (ice) to liquid (water), the specific name for this heat is latent heat of fusion.
It describes the heat required to change a substance from solid to liquid at constant temperature.
Therefore, the correct answer is latent heat of fusion.

When an object moves through a fluid such as air or water, it experiences resistance known as drag.
A pointed front allows the fluid to flow smoothly around the object instead of creating strong opposing forces.
This reduces the frictional resistance and allows the object to move more efficiently.
As a result, less energy is required to maintain motion.
Therefore, the pointed front helps to reduce the friction of the fluid.

When pressure is constant, the volume of a gas is directly proportional to its absolute temperature according to Charles’ law.
This relationship is expressed as
\[\frac{V_1}{T_1} = \frac{V_2}{T_2}\]
The temperatures must be converted to Kelvin.
Initial temperature:
\[T_1 = 0^\circ C + 273 = 273 \, K\]
Final temperature:
\[T_2 = 273^\circ C + 273 = 546 \, K\]
Substituting the values,
\[\frac{200}{273} = \frac{V_2}{546}\]
Multiplying both sides by 546,
\[V_2 = \frac{200 \times 546}{273}\]
\[V_2 = 200 \times 2\]
\[V_2 = 400 \, m^3\]
Therefore, the new volume is 400 m\(^3\).

As a pendulum swings, its energy continuously changes between potential energy and kinetic energy.
At the highest points of the swing, the pendulum momentarily stops before changing direction, so its velocity is zero and kinetic energy is zero.
As it moves downward, its speed increases and its potential energy decreases while kinetic energy increases.
The maximum speed occurs at the lowest point, which is the equilibrium position.
Since kinetic energy depends on speed, it is greatest at this lowest point.
Therefore, the maximum kinetic energy occurs at point Q.

In doped semiconductors, impurities are added to improve electrical conductivity.
These impurities either provide extra electrons or create spaces where electrons can move.
The negatively charged particles responsible for conduction are electrons, while the positively charged absence of electrons are called holes.
Both electrons and holes contribute to the flow of electric current.
Therefore, the charge carriers in doped semiconductors are electrons and holes.

Magnetic shielding works by using a material that can easily attract and guide magnetic field lines through itself instead of allowing them to pass into the protected region.
Materials with high magnetic permeability are very effective for this purpose because they provide an easier path for magnetic field lines.
Soft iron has very high magnetic permeability, so magnetic field lines prefer to pass through it rather than through the surrounding space.
This reduces the magnetic field in the region being protected.
Therefore, soft iron is commonly used for magnetic shielding.