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R.D = \(\frac{\text {weigh in air - weigh in liquid X}}{\text {weigh in air - weigh in water}}\) = \(\frac{10 - 7}{10 - 6} = \frac{3}{4}\)

Calculation of velocity: V = \sqrt[V\(^2\)x + V\(^2\)\(_y\)] V\(_x\) = 40 Cos30 = 34.6 m/s V\(_y\) = 40 sin30 - 10(1) = 10 m/s V = \sqrt[34.6\(^2\) + 10\(^2\)] V = 36.02m/s

Using; \(m_1\) \(u_1\) + \(m_2\) \(u_2\) = (\(m_1\) + \(m_2\))v \(m_1\) = 0.5kg, \(u_1\) = 10ms\(^{1}\), \(m_2\) = 0.5kg, \(u_1\) = 0 \(\therefore\) (0.5kg x 10) + (0.5 x 0) = (0.5 + 0.5)v v = 5ms\(^{1}\)

Given \(m_1\) = 0.05kg, \(u_1\) = 200ms\(^{-1}\), \(m_2\) = 0.95kg K.E = \(\frac{1}{2}\)\(m_r\)v\(^{2}\) \(m_1\)\(u_1\) = v(\(m_1\) + \(m_2\)) [law of conversation of momentum] v = \(\frac{0.05 \times 200}{0.05 + 95}\) = 10ms\(^{-1}\) K.E = \(\frac{1}{2}\)(1)10\(^{2}\) = 50J

In simple harmonic motion, the acceleration of the particle is directed towards its mean position and directly proportional to its displacement.

Frictional force opposes motion

Surface tension decreases by: * Increasing liquid's temperature * Adding soap to the liquid

Young's modulus \(\frac{stress}{strain}\) Strain = \(\frac{e}{l} = \frac{0.05}{10} = \frac{10^{7}}{0.005}\) 2 x 10\(^{9}\)Nm\(^{-2}\)

, displacement, velocity, and acceleration, linear momentum, force are vector quantities, while speed (the magnitude of velocity), time, and mass are scalars. To qualify as a vector, a quantity having magnitude and direction must also obey certain rules of combination.

Pressure varies inversely as A i.e P \(\propto\) \(\frac{1}{A}\)

The collision between the gases is perfectly elastic

Using \(\frac{P_{1}}{T_{1}} = \frac{P_{2}}{T_{2}}\) \(P_1\) = 80Nm\(^{2}\) \(T_1\) = 47 + 273 = 320k \(T_2\) = 27 + 273 = 300k \(P_2\)? \(\therefore\) = \(P_2\) = \(\frac{P_{1}T_{2}}{T_{1}}\) = \(\frac{80 \times 300}{320}\) = 75.Nm\(^{2}\)

\(p_1\) = \(P_0\), \(V_1\) = \(V_0\), \(V_2\) = \(\frac{1}{5}\)\(V_0\) \(P_2\) = ? \(P_1\)\(V_1\) = \(P_2\)\(V_2\) \(P_2\) = \(\frac{P_{1}V_{1}}{V_{1}}\) = \(\frac{\not P_{o}V_{o}}{\frac{1}{5}P_{o}}\) = 5\(\not P_{o}\)

The rate of evaporation depends on temperature, presence of wind, the humidity of the surrounding, and the surface area of the liquid exposed to the atmosphere. It doesn't depend on the mass of the liquid. The larger the surface area, the more would be the rate of evaporation.

Thermistors act as a passive component in a circuit. They are an accurate, cheap, and robust way to measure temperature.