Physics 2024 Jamb Examination

Upthrust is equal to the weight of the fluid displaced (Archimedes' Principle). \[ \text{Upthrust} = V \rho g \] \[ \text{Upthrust} = (4.2 \times 10^{-4}) \times 1028 \times 10 \] \[ \text{Upthrust} = 4.2 \times 10^{-3} \times 1028 \approx 4.3176\,N \]

Using Boyle's Law (P\(_1\)V\(_1\) = P\(_2\)V\(_2\)): \[ 10^5 \times 20 = (4 \times 10^5) \times V_2 \] \[ V_2 = \frac{20 \times 10^5}{4 \times 10^5} = 5\,m^3 \]

1. Total Power = \( 80 + 100 + 120 = 300\,W = 0.3\,kW \) 2. Energy per day = \( 0.3\,kW \times 6\,h = 1.8\,kWh \) 3. Energy per month = \( 1.8 \times 31 = 55.8\,kWh \) 4. Total Bill = \( 55.8 \times 24.08 \approx 1343.66 \)

The angle given is 30º to the vertical, which means the angle to the horizontal is \( 90 - 30 = 60^\circ \). The horizontal (effective) component is \( T \cos 60^\circ \): \[ T \cos 60^\circ = 15 \] \[ T(0.5) = 15 \implies T = 30\,N \]

Newton's Law of Cooling states that the rate of loss of heat is proportional to the temperature difference between the body and its surroundings. This is an approximation that holds true only for small temperature differences.

Melting is the process where a solid turns into a liquid as its thermal energy increases.

A pinhole camera works on the principle of the rectilinear propagation of light. The size of the pinhole significantly affects the quality of the image produced. When the hole of a pinhole camera is diminished (made smaller), fewer rays of light from each point on the object can pass through to the screen. This reduction in the overlapping of light rays results in an image that is much sharper and clearer because the 'blur circles' formed on the screen are smaller. However, as the hole becomes smaller, the total amount of light entering the camera decreases, which usually makes the image less bright, but the primary physical advantage of a smaller hole is the increase in sharpness (clarity). Therefore, both clarity and sharpness are enhanced by a smaller pinhole.

Expansivity of materials occurs in three dimensions: linear (\(\alpha\)), area (\(\beta\)), and cubic (\(\gamma\)). These are related based on the dimensionality of the expansion. For most isotropic solids, the relationship is: \[ \gamma = 3\alpha \] \[ \beta = 2\alpha \] Given the cubic expansivity \(\gamma = 3.9 \times 10^{-6} \, \text{K}^{-1}\): First, find the linear expansivity \(\alpha\): \[ \alpha = \frac{\gamma}{3} = \frac{3.9 \times 10^{-6}}{3} = 1.3 \times 10^{-6} \, \text{K}^{-1} \] Next, calculate the area expansivity \(\beta\): \[ \beta = 2\alpha = 2 \times (1.3 \times 10^{-6}) = 2.6 \times 10^{-6} \, \text{K}^{-1} \] This shows that area expansion is two-thirds of the cubic expansion for the same material.

In alternating current (AC) circuits, impedance (represented by the symbol \(Z\)) is the total opposition that a circuit offers to the flow of current. It combines the effects of ordinary resistance (\(R\)) and reactance (\(X\)). Since impedance is effectively a 'complex' form of resistance that limits current flow, it is measured in the same unit as resistance, which is the Ohm (represented by the Greek letter \(\Omega\)). The other units provided represent different physical quantities: Tesla (T) for magnetic flux density, Henry (H) for inductance, and Watt (W) for power.

This relationship can be analysed using the equations of motion. If displacement (\(s\)) is proportional to the square of time (\(t^2\)), we can write the relationship as: \[ s = kt^2 \] where \(k\) is a constant. We can find the velocity (\(v\)) by differentiating displacement with respect to time: \[ v = \frac{ds}{dt} = 2kt \] To find the acceleration (\(a\)), we differentiate the velocity with respect to time: \[ a = \frac{dv}{dt} = 2k \] Since \(2k\) is a constant, the acceleration does not change with time. This matches the standard kinematic equation for an object starting from rest: \(s = \frac{1}{2}at^2\). Therefore, the car is moving with uniform (constant) acceleration.