2. एक ही दिशा में चल रहे दो रेल इंजन जिनका वज़न 120 kN व 100 kN हैं, टकराने के पश्चात् एक साथ आगे बढ़ते हैं । टक्कर के पश्चात् समान गति (speed) होगी \( \begin{array}{ll}\text { (1) } 3.8 \mathrm{~m} / \mathrm{s} & \text { (2) } 3.9 \mathrm{~m} / \mathrm{s} \\ \text { (3) } 4.0 \mathrm{~m} / \mathrm{s} & \text { (4) } 4.1 \mathrm{~m} / \mathrm{s}\end{array} \)

a) Use the kinetic theory of gases to explain the pressure in the gas b) Hence discuss the effect on the pressure of the gas when the gas is heated at constant volume c) On the same axes of a p-V graph, show the change in the pressure of the gas when the gas is heated at constant volume and when the volume of the gas is reducod at constant temperature.

If the component vector \( \vec{A} \) along the direction of vector \( \vec{B} \) is zero, what can you conclude abot the vectors? a) Is it possible to add a vector quantity to a scalar quantity? Explain b) Can the magnitude of a vector have a negative value? Explain Which of the following physical quantities are vector \& which are not: force, temperature, th volume of water in a can, the ratings of a TV show, the height of a building, the velocity of

10. Hajmi \( 50 \mathrm{~cm}^{3} \) bo lgan alyumin sharning massasi 135 g . Agar \( 1 \mathrm{cmm}^{3} \) alyuminning massasi \( 1 \mathrm{~cm}^{3} \) temiming massasidan \( 5,2 \mathrm{~g} \) kam bo'lsa, shunday hajmdagi temir sharning massasi qancha bo ladi?

6. A particle undergoes three consecutive displacements: \( \bar{d}_{1}=(15 i+30 j+12 k) \mathrm{cm} \). \( \vec{d}_{2}=(23 i-14 j-5 k) a n \) and \( \vec{d}_{3}=(-13 i+15 j) \) an Find the magnitude of the resultant displacement.

9.4. (a) Suppose that the unknown resistance \( R_{u} \) in Figure 9.2 is a resistance thermometer whose resistance at \( 100^{\circ} \mathrm{C} \) is \( 500 \Omega \) and whose resistance varies with temperature Chapter 9 at the rate of \( 0.5 \Omega /{ }^{\circ} \mathrm{C} \) for small temperature changes around \( 100^{\circ} \mathrm{C} \). Calculate the sensitivity of the total measurement system for small changes in temperature around \( 100^{\circ} \mathrm{C} \), given the following resistance and voltage values measured at \( 15^{\circ} \mathrm{C} \) by instruments calibrated at \( 15^{\circ} \mathrm{C}: R_{1}=500 \Omega ; R_{2}=R_{3}=5000 \Omega \); \( V_{i}=10 \mathrm{~V} \)