0.20
Using Raoult's law, the partial pressures are \( P_{\text{toluene}} = 0.4 \times 3.63 \, \text{kPa} = 1.452 \, \text{kPa} \) and \( P_{\text{benzene}} = 0.6 \times 9.7 \, \text{kPa} = 5.82 \, \text{kPa} \). The total pressure is \( P_{\text{total}} = 1.452 + 5.82 = 7.272 \, \text{kPa} \). The mole fraction of toluene in the vapour phase is \( \frac{1.452}{7.272} \approx 0.20 \).
A constant force of \[ \mathbf{F} = (8\hat{i} - 2\hat{j} + 6\hat{k}) \text{ N} \] acts on a body of mass 2 kg, displacing it from \[ \mathbf{r_1} = (2\hat{i} + 3\hat{j} - 4\hat{k}) \text{ m to } \mathbf{r_2} = (4\hat{i} - 3\hat{j} + 6\hat{k}) \text{ m}. \] The work done in the process is:
A ball 'A' of mass 1.2 kg moving with a velocity of 8.4 m/s makes a one-dimensional elastic collision with a ball 'B' of mass 3.6 kg at rest. The percentage of kinetic energy transferred by ball 'A' to ball 'B' is:
A metre scale is balanced on a knife edge at its centre. When two coins, each of mass 9 g, are kept one above the other at the 10 cm mark, the scale is found to be balanced at 35 cm. The mass of the metre scale is:
A body of mass \( m \) and radius \( r \) rolling horizontally with velocity \( V \), rolls up an inclined plane to a vertical height \( \frac{V^2}{g} \). The body is: