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 \( 15^{\circ} \mathrm{C}: R_{1}=500 \Omega ; R_{2}=R_{3}=5000 \Omega \); \( V_{i}=10 \mathrm{~V} \)

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?

ercice résolu Un corps solide \( (\mathrm{S}) \) de masse \( \mathrm{m}=2,9 \mathrm{~kg} \) glisse avec une vitesse constante \( \mathrm{v}=3,7 \mathrm{~m} / \mathrm{s} \) sur un plan incliné d'un gle \( \theta=35^{\circ} \) par rapport à l'horizontale. Le corps \( (\mathrm{S}) \) est soumis à une force \( \overrightarrow{\mathrm{F}} \) dont la direction est parallèle à la ne de plus grande pente, et de sens opposé à celui du mouvement du corps ( S ) et d'intensité \( \mathrm{F}=1,57 \mathrm{~N} \). On lige les frottements et on prend \( \mathrm{g}=9,8 \mathrm{~N} / \mathrm{kg} \). 1- Faire un schéma de la situation et y représenter les vecteurs forces extérieurs sans respect de l'echelle. 2- Le centre de gravité G du corps solide \( (\mathrm{S}) \) se déplace d'une distance \( \mathrm{AB}=4,7 \mathrm{~m} \). 2.1. Le travail de \( \overrightarrow{\mathrm{F}} \) entre A et B , est-il moteur ou résistant ? Justifier votre réponse. 2.2. Calculer \( \mathrm{W}_{\mathrm{A} \rightarrow \mathrm{B}}(\overrightarrow{\mathrm{F}}) \) et \( \mathrm{W}_{\mathrm{A} \rightarrow \mathrm{B}}(\overrightarrow{\mathrm{P}}) \).

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 \( 15^{\circ} \mathrm{C}: R_{1}=500 \Omega ; R_{2}=R_{3}=5000 \Omega \); \( V_{i}=10 \mathrm{~V} \)

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 \( \begin{array}{ll}\text { (1) } 3.8 \mathrm{~m} / \mathrm{s} & \text { (2) } 3.9 \mathrm{~m} / \mathrm{s} \\ \text { (3) } 4.0 \mathrm{~m} / \mathrm{s} & \text { (4) } 4.1 \mathrm{~m} / \mathrm{s}\end{array} \)

The velocity of a canoe in a river without the current would be \( \langle 8,6) \). However, the current is flowing north to south at a speed of 2 miles per hour. What is the actual velocity vector of the canoe? \[ (10,6) \] \( (8,4) \) \( (6,8) \)