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F = ke k = \(\frac{F_1}{e_1}\) F\(_1\) = 10N, e\(_1\) = 0.02m F\(_2\) = 40N, e\(_2\) = ? \(\frac{F_1}{e_1}\) = \(\frac{F_2}{e_2}\) \(\frac{10}{0.02}\) = \(\frac{40}{e_2}\) e\(_2\) = \(\frac{40 \times 0.02}{10}\) = 0.08m The new length = 1 + 0.08 = 1.08m

The term with a different dimension from the others is D. Torque, as its dimensions ML\(^2\)T\(^{−2}\) which differ from the dimensions of stress and pressure, which are ML\(^{−1}\)T\(^{−2}\)

(a) SURFACE TENSION = \(\frac{\text{force}}{\text{length}}\) FORCE = mass x accel. due to gravity Dimension of force = M.LT\(^{-2}\) Dimension of length = L Dimension of surface area = \(\frac{MLT^{-2}}{L}\) = MT\(^{-2}\) (b) The instruments used for measuring the force of gravity at a place are: (1) Gravimeter, (2) Spring balance, (3) Gravitational accelerometer.

(i) Stress: The base unit of stress is the Pascal (Pa), which is equivalent to kg⋅m\(^{−1}\)⋅s\(^{−2}\) (ii) Force Constant (Spring Constant,k): The base unit of the spring constant is also in Newtons per meter (N/m), which is equivalent to kg⋅s\(^{−2}\) (iii) Planck's Constant (h): The base unit of Planck's constant is Joule seconds (J·s), which is equivalent to kg⋅m\(^2\)s\(^{−1}\) .

Aneroid barometers are compact and lightweight, making them suitable for use in aircraft where space and weight are critical considerations. They provide a reliable measurement of altitude based on changes in atmospheric pressure.

When boiling water is poured into the tumbler, the inner surface heats up and expands quickly, while the outer surface remains cooler and expands more slowly. This difference in expansion rates creates stress in the glass, leading to cracks.

From pressure law \(\frac{P_1}{T_1} = \frac{P_2}{T_2}\) P\(_2\) = \(\frac{P_1 \times T_2}{T_1}\) P\(_1\) = 40mmHg, P\(_2\) = ? T\(_1\) = 298k, T\(_2\) = 348k \(\frac{40}{298} = \frac{P_2}{348}\) P\(_2\) = \(\frac{40\times348}{298}\) = 46.71mmHg

D. Liquid-in-glass thermometer. In a liquid-in-glass thermometer, the liquid (usually mercury or colored alcohol) expands and contracts with temperature changes, allowing for the measurement of temperature based on the volume change of the liquid.

Boyle's law states that at a constant temperature, the pressure of a gas is inversely proportional to its volume (P ∝\(\frac{1}{V}\) This relationship is fundamental when calculating the work done during the isothermal expansion or compression of a gas, as it directly involves changes in volume and pressure

Temperature only. This means that the average kinetic energy is directly related to the gas's absolute temperature. The relationship can be defined by the equation: K.E = \(\frac{3}{2}\)kT where K.E = average kinetic energy, k = Boltzmann's constant, and T = absolute temperature.

Using \(^0\)F = ( \(^0\) C x \(\frac{9}{5}\)) + 32 → ( ºc x 1.8 ) + 32. \(^0\) C = 60º Then, Using \(^0\)F = ( 60 x \(\frac{9}{5}\)) + 32 = 108 + 32 = 140ºF

Absolute zero is the lowest possible temperature where molecular motion is minimal. At this temperature, the kinetic energy of the molecules is effectively zero, meaning they do not have enough energy to move.

Water is not suitable for use as a thermometric liquid because: a) It wets glass: This can cause issues with reading the level of the liquid. b) It needs to be coloured: Water is typically clear, making it difficult to see the level without coloring. c) It has a low density: This can affect the sensitivity and accuracy of the thermometer.

Using \(P_1\) \(V_1\) = \(P_2\) \(V_2\) \(V_2\) = \(\frac{P_1\times V_2}{P_2}\) \(V_2\) = \(\frac{10^5\times 20}{4 \times 10^5}\) \(V_2\) = 5m\(^3\)

Using the general gas equation; \(\frac{P_1 \times V_1}{T_1}\) = \(\frac{P_2 \times V_2}{T_2}\) P\(_1\) = P, P\(_2\) = 2P, T\(_1\) = 27ºC → 300K, T\(_2\) = 127ºC → 400k, V\(_2\) = \(\frac{P_1 \times V_1 \times T_2}{T_1 \times P_2}\) V\(_2\) = \(\frac{P \times V_1 \times 400}{300 \times 2P}\) = \(\frac{2V_1}{3}\) \DeltaV = V\(_1\) - \(\frac{2V_1}{3}\) = \(\frac{V_1}{3}\) Therefore, The volume decreases by \(\frac{1}{3}\) of the original volume.