Physics 2019 Jamb Examination

Stable equilibrium occurs when an object is in its lowest possible energy state.

When the body is slightly displaced, its center of gravity (CG) rises, which leads to an increase in its potential energy \( (P.E. = mgh) \). When released, the gravitational force creates a restoring moment that returns the body to its original position.

A standard meter rule has a smallest graduation of \( 1 \, \text{mm} \) or \( 0.1 \, \text{cm} \). While a user might estimate 'half a division' (\( 0.05 \, \text{cm} \)), it is impossible to accurately determine a reading with a precision of two arbitrary decimal places like 2.56cm (\( 0.06 \, \text{cm} \)). Most laboratory measurements with a meter rule are recorded to one decimal place.

Charles' Law states that for a fixed mass of gas at constant pressure, the volume V is directly proportional to its absolute temperature T (in Kelvin). Mathematically: \[ V \propto T \implies \frac{V}{T} = \text{constant} \] The graph representing this relationship is a straight line passing through the origin (0,0) on a V - T plot, which corresponds to Graph I.

Hare's apparatus is used to compare the densities of two liquids based on the principle that pressure at the same horizontal level in a continuous fluid is equal. The relationship is given by: \[ h_1 \rho_1 = h_2 \rho_2 \] Where: \( h_w = 20.0 \; \text{cm} \) (height of water) \( \rho_w = 1.0 \; \text{g/cm}^3 \) (density of water) \( \rho_k = 0.80 \; \text{g/cm}^3 \) (density of kerosene) \[ 20.0 \times 1.0 = h_k \times 0.80 \] \[ h_k = \frac{20.0}{0.80} = 25.0 \; \text{cm} \]

In a plane mirror, the image is as far behind the mirror as the object is in front. If the girl moves toward the mirror at speed \( v \), the image also moves toward the mirror from the opposite side at speed \( v \). The relative speed (the rate at which the distance between them closes) is the sum of their speeds: \[ \text{Relative speed} = v + v = 4.0 + 4.0 = 8.0 \; \text{m/s} \]

Work done or energy is defined as the product of Force and Displacement. The SI unit of Force is the Newton (N) and the SI unit of displacement is the Meter (m). Therefore: \[ 1 \; \text{Newton} \times 1 \; \text{Meter} = 1 \; \text{Newton-meter} = 1 \; \text{Joule (J)} \]

When an object is viewed through a glass slab, it appears to be raised due to refraction. The refractive index (\( n \)) can be calculated using the formula: \[ n = \frac{\text{Real depth}}{\text{Apparent depth}} \] Or, using the 'apparent shift' (the distance the microscope was raised): \[ n = \frac{\text{Real depth}}{\text{Real depth} - \text{Apparent shift}} \] Given: Real depth (thickness) = 2 cm Apparent shift = 0.67 cm \[ n = \frac{2}{2 - 0.67} = \frac{2}{1.33} \approx 1.50 \]

Radio waves are a type of electromagnetic (EM) radiation. All electromagnetic waves, including light, radio waves, X-rays, and microwaves, travel at the same constant speed in a vacuum (the speed of light), which is approximately \( 3 \times 10^8 \; \text{m/s} \).

The 'resultant' is a single vector that represents the combined effect of two or more vectors. Conversely, an 'equilibrant' is a force equal in magnitude but opposite in direction to the resultant, which keeps the system in equilibrium.

To find the polarity of a solenoid, we use the Right-Hand Grip Rule for coils. Wrap your fingers in the direction of the current; your thumb points toward the North pole. Looking at the diagram, if current flows from A to B, and the winding goes 'over the top' toward B, the thumb points toward B. Thus, B becomes the North pole and A becomes the South pole.