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Heat gained by 25º C body = Heat lost by 35º C body M\(_c\) c \(\delta\)\(\theta\) = M\(_h\) c\(\delta\)\(\theta\) 70 x c x (f - 25) = 70 x c x (35 - f) where f = final temperature f - 25 = 35 - f (f and 70 cancel out) 2f = 35 + 25 = 60 f = \(\frac{60}{2}\) = 30ºC

specific heat capacity of water = 4200Jkg\(^{-1}\)k\(^{-1}\), Specific heat of vaporization of water = 2.26 x 10\(^6\)Jkg\(^{-1}\), mass of water = 0.02kg, water vapour temp. = 100ºC, water at 97ºC The amount of heat required = ML + Mc\Delta\(\theta\) = 0.02 x 2.26 x 10\(^6\) + 0.02 x 4200 x (100 - 97) = 45,200 + 252 = 45,452J.

Relative humidity = \(\frac{\text{S.V.P at dew point}}{\text{S.V.P at air temperature}}\) S.V.P at dew point = 7.3mmHg S.V.P at air temperature = 13.5mmHg R.H = \(\frac{7.3}{13.5}\) x 100 \(\approxeq\) 54%

In a saturated vapour, the rate of evaporation (y) equals the rate of condensation (x). This means that the amount of vapor entering the gaseous phase is equal to the amount of vapour returning to the liquid phase, resulting in a stable concentration of vapour in the air.

Newton's Law of Cooling states that the rate of heat loss of an object is directly proportional to the difference in temperature between the object and its surroundings, provided that this temperature difference is small. Therefore, this law is only valid within a small temperature range.

When thermal energy is increased, the change in state is called melting (solid to liquid) or vaporization (liquid to gas), depending on the initial and final states of the substance.

The constant temperature at which a liquid changes into gaseous state is known as its boiling point.

Gravitational force Fg = \(\frac{Gm_1m_2}{r^2}\) Fg = 10N distance = \(\frac{r}{2}\) F'g = \(\frac{Gm_1m_2}{(\frac{r}{2})^2}\) = 4 (\(\frac{Gm_1m_2}{r^2}\)) = 4Fg = 4 x 10 = 40N

Gravitational force Fg = \(\frac{Gm_1m_2}{r^2}\) = 6.67N \(m_1\) = 10\(^{24}\)kg, \(m_2\) = 10\(^{27}\)kg, G = 6.6 x 10\(^{-11}\)Nm\(^2\)kg\(^{-2}\) and r = ? 6.67 = \(\frac{ 6.6\times 10^{-11}\times10^{24}\times10^{27}}{r^2}\) 6.67r\(^2\) = 6.6 x 10\(^{40}\) r\(^2\) = \(\frac{6.6\times10^{40}}{6.67}\) \(\approx\) 9.89 \times 10\(^{39}\) r = \(\sqrt{ 9.89\times10^{39}}\) \(\approxeq\) 9.94 \times 10\(^{19}\)m → 1.0 x 10\(^{20}\)m

Ebonite rods are negatively charged, while glass rods are positively charged when rubbed. Opposite charges attract each other, leading to an attractive force between the rods.

The magnetic force on an electron in a magnetic field (F) = q v Bsin\(\theta\) B = 10T, q = 3 x 10\(^7\)m/, \(\theta\) = 60º and q = 1.6 x 10\(^{-19}\)C F = 1.6 x 10\(^{-19}\) x 3 x 10\(^7\) x 10 x sin 60º \(\approxeq\) 4.162 \times 10\(^{-11}\)N

The device for measuring the angle of dip is called a dip circle or declinometer. A dip circle contains a magnetic needle that can move freely, enabling it to align with the Earth's magnetic field. The angle formed between the needle and the horizontal plane represents the angle of dip.

Voltage across shunt = Voltage across galvanometer I\(_s\)R\(_s\) = I\(_g\)R\(_g\) R\(_g\) = 5\(\Omega\), I\(_g\) = 10mA = 0.01A, I\(_s\) = 2 - 0.01 = 1.99A R\(_s\) = \(\frac{I_g \times R_g}{I_s}\) = \(\frac{0 .01 \times 5}{1.99}\) = 0.025\(\Omega\)

Keepers reduce self-demagnetization of magnets by providing a low reluctance path for magnetic flux, thereby containing the flux within the keeper.

A dynamo converts mechanical energy into electrical energy using the principle of electromagnetic induction, which is a magnetic effect of electric current.