2025 - JAMB Physics Past Questions and Answers - page 2

Impulse is equal to the change in momentum, and momentum is defined as mass multiplied by velocity. Therefore, impulse can be written as

\[ \text{Impulse} = m(v - u) \]

The final velocity is first calculated using the equation of motion

\[ v = u + at \]

Substituting the given values gives

\[ v = 4 + (5 \times 2) \]

\[ v = 14 \, \text{m/s} \]

The change in velocity becomes

\[ v - u = 14 - 4 = 10 \, \text{m/s} \]

Since the impulse is given as 60 kgms\(^{-1}\), substitute into the impulse equation

\[ 60 = m \times 10 \]

Solving for the mass gives

\[ m = \frac{60}{10} \]

\[ m = 6 \, \text{kg} \]

Therefore, the mass of the body is 6 kg.

An annular eclipse takes place when the Sun, Moon, and Earth lie along the same straight line. In this arrangement, the Moon comes between the Earth and the Sun.

However, the Moon is farther away from the Earth than usual, so its apparent size becomes smaller than that of the Sun. Because of this, the Moon cannot completely block the Sun.

As a result, a bright ring of sunlight remains visible around the Moon.

Therefore, an annular eclipse is formed when the Sun, Moon, and Earth are aligned in a straight line.

When steam condenses, heat is released due to two processes. First, heat is released during condensation, and second, additional heat is released when the condensed water cools from 100ºC to 15ºC.

The total heat released is expressed as

\[ Q = m \left(L_v + c(100 - 15)\right) \]

The temperature difference is

\[ 100 - 15 = 85 \]

The heat released becomes

\[ Q = m \left(2.26 \times 10^6 + (4200 \times 85)\right) \]

\[ Q = m \left(2.26 \times 10^6 + 357000\right) \]

\[ Q = m (2.617 \times 10^6) \]

The total heat released is given as 5400 kJ, which is converted to joules

\[ Q = 5.4 \times 10^6 \, \text{J} \]

Substituting gives

\[ 5.4 \times 10^6 = m (2.617 \times 10^6) \]

\[ m = \frac{5.4 \times 10^6}{2.617 \times 10^6} \]

\[ m \approx 2.06 \, \text{kg} \]

Therefore, the mass of water collected is 2.06 kg.

In short-sightedness, distant objects cannot be focused on the retina because the eye forms the image in front of the retina. The far point represents the maximum distance at which the eye can see clearly, which is 95 cm in this case.

To correct this defect, a lens must form a virtual image of distant objects at the far point. For distant objects, the object distance is effectively infinite.

The lens formula is written as

\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \]

Since the object is at infinity, the second term becomes zero

\[ \frac{1}{f} = \frac{1}{-95} \]

\[ f = -95 \, \text{cm} \]

The negative sign indicates a diverging lens.

Therefore, the defect is corrected using a diverging lens of focal length 95 cm.

Tension is a force acting along a string. Since tension is a type of force, its dimensions are the same as those of force.

Force is defined using Newton’s second law as mass multiplied by acceleration

\[ F = ma \]

The dimension of mass is \([M]\) and the dimension of acceleration is \([LT^{-2}]\). Multiplying these gives

\[ [F] = [M][LT^{-2}] \]

\[ [F] = [MLT^{-2}] \]

Since tension is a force, its dimensional formula is also \([MLT^{-2}]\).

An object placed in water experiences an upward force called upthrust. Whether it sinks or floats depends on the comparison between its weight and the upthrust.

If the density of the object is greater than the density of water, the weight of the object becomes greater than the upthrust acting on it.

Because the upward force is insufficient to support it, the object moves downward and sinks.

Therefore, an object sinks when its density is greater than that of water.

When pressure remains constant, Charles’ law states that the volume of a gas is directly proportional to its absolute temperature.

This relationship is written as

\[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \]

The initial temperature must first be converted to Kelvin

\[ T_1 = 57 + 273 = 330 \, K \]

The new volume is one-fifth of the original volume, so

\[ \frac{V_2}{V_1} = \frac{1}{5} \]

Substituting into Charles’ law gives

\[ T_2 = 330 \times \frac{1}{5} \]

\[ T_2 = 66 \, K \]

Converting back to Celsius gives

\[ T_2 = 66 - 273 \]

\[ T_2 = -207^\circ C \]

Therefore, the new temperature is \(-207^\circ C\).

The capacitance of a parallel plate capacitor is given by the formula

\[ C = \epsilon_0 \frac{A}{d} \]

The radius is converted to metres

\[ r = 6 \, \text{cm} = 0.06 \, \text{m} \]

The separation is also converted

\[ d = 0.12 \, \text{cm} = 0.0012 \, \text{m} \]

The area of the plate is calculated using

\[ A = \pi r^2 \]

\[ A = 3.142 \times (0.06)^2 \]

\[ A = 3.142 \times 0.0036 \]

\[ A = 0.01131 \, \text{m}^2 \]

Substituting into the capacitance formula gives

\[ C = 8.85 \times 10^{-12} \times \frac{0.01131}{0.0012} \]

\[ C = 8.85 \times 10^{-12} \times 9425 \]

\[ C \approx 8.34 \times 10^{-11} \, F \]

Therefore, the capacitance is \(8.3 \times 10^{-11} \, F\).

The pressure law states that pressure is directly proportional to absolute temperature when volume remains constant.

This relationship can be written as

\[ P \propto T \]

For a graph to pass through the origin, both pressure and temperature must become zero at the same point.

This condition is satisfied only when temperature is measured on an absolute scale, where zero represents the complete absence of thermal energy.

The thermodynamic scale, also known as the Kelvin scale, is such an absolute scale.

Therefore, the correct temperature scale is the thermodynamic scale.

Density is defined as mass divided by volume, so volume can be found by rearranging the formula as \( \text{Volume} = \frac{\text{Mass}}{\text{Density}} \).
For the ice, the mass is 90g and the density is 0.9g/cm\(^3\). Substituting gives \( \text{Volume of ice} = \frac{90}{0.9} = 100 \, \text{cm}^3 \).
After melting, the mass remains the same but the density becomes that of water, which is 1g/cm\(^3\). Using the same formula gives \( \text{Volume of water} = \frac{90}{1} = 90 \, \text{cm}^3 \).
The change in volume is obtained by subtracting the final volume from the initial volume. This gives \( 100 - 90 = 10 \, \text{cm}^3 \).
This shows that the volume decreases by 10cm\(^3\).
Therefore, the change in volume is 10cm\(^3\) decrease.