JAMB Physics 2015 Past Questions & Answers

This question requires the use of the combined gas law, which is (P₁V₁)/T₁ = (P₂V₂)/T₂. First, convert all temperatures to Kelvin by adding 273, so T₁ = 27°C + 273 = 300K and T₂ (at S.T.P.) = 0°C + 273 = 273K. The initial conditions are P₁ = 800mmHg and V₁ = 76cm³, while the final conditions at S.T.P. are P₂ = 760mmHg and T₂ = 273K. Rearranging the formula to find the new volume V₂ gives V₂ = (P₁V₁T₂) / (P₂T₁), which is (800 x 76 x 273) / (760 x 300) = 72.8cm³.

Common mistake: The most common mistake is forgetting to convert the temperatures from Celsius to Kelvin before using them in the combined gas law formula, as all gas law calculations require absolute temperature.

Boyle's law describes the relationship between the pressure and volume of a fixed mass of gas at a constant temperature. The law states that pressure (P) is inversely proportional to volume (V), which means their product is always a constant value (PV = constant). Therefore, for an initial state (P1, V1) and a final state (P2, V2) of the same gas under these conditions, the relationship is P1V1 = P2V2.

Common mistake: Students often confuse Boyle's law with the combined gas law (P1V1/T1 = P2V2/T2) and mistakenly choose an option that includes temperature, like the incorrect formula presented in option D.

In optics, a 'ray' is the term used to represent the path that light travels along. It is drawn as a straight line with an arrow to indicate the direction of light propagation. This concept is fundamental for studying how light interacts with mirrors and lenses.

Common mistake: Students often mistakenly choose 'Beam' because a beam is what we usually see, but a beam is actually a collection or bundle of many individual light rays.

The formula for inductive reactance $(X_L)$ is $X_L$ = 2πfL, where 'f' is the frequency and 'L' is the inductance. To find the inductance L, we rearrange the formula to L = $X_L$ / (2πf). Substituting the given values, we get L = 1 / (2 * π * (50/π)). The 'π' in the numerator and denominator cancels out, leaving L = 1 / $(2 * 50)$, which simplifies to L = $1/100$ or 0.01 H.

Common mistake: A common mistake is to wrongly calculate 2πf / $X_L$ instead of $X_L$ / (2πf), which results in the incorrect answer of 100 H.

A stroboscope is an instrument that produces flashes of light at a specific frequency. When used to view a wave, if the frequency of the light flashes is set to be the same as the frequency of the wave, the wave is illuminated at the same point in its cycle every time. This creates an optical illusion, making the moving wave appear to be frozen in place or stationary.

Common mistake: Students might mistakenly choose 'Ripple' or 'Dipper' because these are often used with stroboscopes in a ripple tank experiment, but they are the wave itself or its source, not the effect the stroboscope creates.

An elastic collision is a special type of collision where two key quantities do not change. Firstly, the total linear momentum of the objects before they collide is equal to their total linear momentum after they collide, so momentum is conserved (IV). Secondly, the total kinetic energy of the objects is also the same before and after the collision, meaning kinetic energy is conserved (I). Therefore, both statements I and IV are correct for an elastic collision.

Common mistake: Students often mistakenly choose option A because they remember that energy conservation is what makes a collision elastic, but they forget that linear momentum is conserved in both elastic and inelastic collisions.

According to the law of flotation, which is based on Archimedes' principle, an object will float in a fluid when the upward buoyant force acting on it is equal to its own weight. This buoyant force is also equal to the weight of the fluid displaced by the object. Therefore, for an object to float, it must displace a weight of the fluid that is exactly equal to its own weight.

Common mistake: Students often mistakenly choose option A, confusing the condition for floating with the fact that a fully submerged object displaces its own volume; a floating object often displaces only a fraction of its total volume.

The general gas law is a combination of Boyle's Law (P is proportional to 1/V), Charles' Law (V is proportional to T), and the Pressure Law (P is proportional to T). When these are combined for a fixed mass of gas, they give the relationship that the product of pressure (P) and volume (V), divided by the absolute temperature (T), is a constant. This is written mathematically as PV/T = a constant.

Common mistake: Students often mistakenly choose option B (PV = a constant) because they remember Boyle's Law, but they forget that the general gas law must also include the relationship with temperature (T).

The 'pool of water' seen on a hot road is an optical illusion called a mirage. On a sunny day, the air near the road surface is very hot and less dense than the cooler air above it. Light rays from the sky bend (refract) as they pass from the cooler, denser air into the hotter, less dense air, and are bent upwards towards the observer's eye. The brain interprets this light as coming from the ground, creating an image of the sky that looks like a reflection in water.

Common mistake: Students might be tempted to choose option B, thinking it's a psychological effect, but this is a physics question requiring a scientific explanation based on the properties of light.

A luminous object is an object that produces its own light, while a non-luminous object shines by reflecting light from another source. The sun, stars, and a lit candle all produce their own light, making them luminous. The moon, however, does not produce its own light; we only see it because its surface reflects the light coming from the sun.

Common mistake: A common mistake is to think the moon is luminous because it appears bright in the night sky, confusing its brightness with the ability to produce its own light.