Physics 2012 Jamb Examination

The apparent weight of an object immersed in a liquid is the actual weight minus the upthrust exerted by the liquid.
Given: Volume \(V = 1 \; m^3\), Mass \(m = 2 \; kg\), Density of liquid \(\rho = 1 \; kgm^{-3}\), and \(g = 10 \; ms^{-2}\).
Actual weight: \[ W = mg = 2 \times 10 = 20 \; N \] Upthrust on the object: \[ U = \rho V g = 1 \times 1 \times 10 = 10 \; N \] Apparent weight: \[ W' = W - U = 20 - 10 = 10 \; N \] The apparent weight decreases because the buoyant force opposes gravity. This principle explains why objects appear lighter in liquids.

Pressure in a liquid at rest arises due to the weight of the fluid above the point of measurement. The formula for pressure is \( P = \rho g h \), where \( \rho \) is the density of the liquid, \( g \) is the acceleration due to gravity, and \( h \) is the depth below the surface.
From this relationship, pressure depends only on the depth \(h\) and the density \(\rho\). It does not depend on the total mass or surface area of the liquid. Thus, the greater the depth or density, the higher the pressure at that point.

Upthrust is equal to the weight of the displaced air, given by \( U = \rho g V \).
Given: \( \rho = 1.3 \; kgm^{-3}\), \( g = 10 \; ms^{-2}\), and \( V = 300 \; m^{3} \).
Therefore, \[ U = 1.3 \times 10 \times 300 = 3900 \; N \] The upthrust represents the buoyant force acting on the balloon, which enables it to rise when this force exceeds its weight.

A clinical thermometer is designed to measure human body temperature with high precision. It typically contains mercury enclosed in a narrow glass capillary. Mercury expands uniformly with temperature, and the constriction near the bulb prevents mercury from returning after measurement. Therefore, a clinical thermometer is a mercury-in-glass thermometer, not a gas or resistance type.

The increase in length \( \Delta L \) of a solid is given by \( \Delta L = \alpha L \Delta \theta \), where \( \alpha \) is the linear expansivity, \( L \) is the original length, and \( \Delta \theta \) is the temperature change.
For P and Q: \[ \dfrac{\Delta L_P}{\Delta L_Q} = \dfrac{\alpha_P L_P}{\alpha_Q L_Q} = \dfrac{2 \times 3}{3 \times 4} = \dfrac{6}{12} = \dfrac{1}{2} \] Therefore, the increase in length of P to Q is in the ratio 1:2. This shows Q expands more due to its higher expansivity and length.

Using the combined gas law: \( \dfrac{P_1 V_1}{T_1} = \dfrac{P_2 V_2}{T_2} \).
Given: \( P_1 = 700 \; mmHg \), \( V_1 = 2000 \; cm^3 \), \( T_1 = 27°C = 300 \; K \), \( P_2 = 760 \; mmHg \), \( T_2 = 273 \; K \).
Substitute: \[ V_2 = \dfrac{P_1 V_1 T_2}{P_2 T_1} = \dfrac{700 \times 2000 \times 273}{760 \times 300} = 1676.3 \; cm^3 \] The gas contracts because the temperature and pressure are reduced to standard conditions.

The relationship between heat energy, mass, specific heat capacity, and temperature change is given by \( Q = mc\Delta T \).
Given: \( Q = 500 \; J \), \( m = 100 \; g = 0.1 \; kg \), \( c = 4200 \; Jkg^{-1}K^{-1} \).
Therefore, \[ \Delta T = \dfrac{Q}{mc} = \dfrac{500}{0.1 \times 4200} = 1.19°C \] Hence, the temperature of the water increases by approximately 1.2°C when 500 J of heat is supplied.

Evaporation is the process by which molecules escape from the liquid surface into the vapour phase. It increases with temperature, wind, and reduced humidity. Increasing atmospheric pressure, however, hinders evaporation because the higher pressure suppresses the movement of molecules from the surface. Therefore, an increase in pressure reduces the rate of evaporation, while all other factors listed enhance it.

The total heat required to melt ice from −30°C to 0°C and then convert it to water is the sum of the heat to raise its temperature and the latent heat of fusion.\[ Q = mc\Delta \theta + mL \] Given: \( m = 1 \; kg \), \( c = 2.1 \times 10^3 \), \( \Delta \theta = 30 \), and \( L = 3.5 \times 10^5 \).
Substitute: $$ Q = (1 \times 2.1 \times 10^3 \times 30) + (1 \times 3.5 \times 10^5)$$ $$= 6.3 \times 10^4 + 3.5 \times 10^5 = 4.13 \times 10^5 \; J $$Hence, the total heat required is 4.13 × 10⁵ J.

Brownian motion describes the random movement of microscopic particles suspended in a fluid due to collisions with the fluid molecules. It provides direct evidence that matter consists of tiny moving particles. It occurs in both liquids and gases, not only in gases. Therefore, statements I, II, and IV correctly describe Brownian motion, while statement III is incorrect.