Deux charges ponctuelles \( \mathrm{q}_{1}=10 \mu \mathrm{C} \) et \( \mathrm{q}_{2}=30 \mu \mathrm{C} \) sont placées respectivement en A et B distantes de 40 cm . 1) Calcule le module du champ électrique \( \overrightarrow{\mathrm{E}} \) au point M milieu de AB . 2) Détermine le point P de \( [\mathrm{AB}] \) où le champ est nul. 3) Détermine le module du champ électrique \( \overrightarrow{\mathrm{E}} \) a) En un point N situé entre A et B à 10 cm de A . Représente ce champ sur un schéma clair. b) En un point Q situé sur lá médiatrice de AB à 20 cm du milieu M de AB .

प्रश्न 20. एक कण सरल आवर्त गति से एक सरल रेखा पर गतिमान है। जब कण की केन्द्र से दूरी \( x_{1} \) तथा \( x_{2} \) है तथा इसक वेग कमशः \( \nu_{1} \) तथा \( v_{2} \) है। सिद्ध कीजिये कि आवर्त काल होगा

Exercise 2: 1. Obtain the moment of inertia tensor of a thin uniform ring of radius R , and mass M, with the origin of the coordinate system placed at the center of the ring, and the ring lying in the xy plane. 2. Obtain the moment of inertia tensor of a uniform hollow sphere of radius R , and mass M , with the origin of the coordinate system placed at the center of the sphere. Note that this problem can be done by dividing the sphere into a large number of infinitesimally thin rings.

2. Aball is thrown upward with a speed of \( 19.6 \mathrm{~m} / \mathrm{s} \). a. How high doesit go until its upward speed decreases to zero. b. How long does the ball take in this upward trip? \( c \). How long does the ball take to return to the initial position? \( d \). What will be its velocity then

11. A particle is projected into the air at a speed of \( 25 \mathrm{~m} / \mathrm{s} \) at an angle \( 40^{\circ} \) above the horizontal. (a) How long does it take the particle to reach its maximum height? (b) What is its horizontal distance covered? 12. A stone is projected with a speed of \( 17.32 \mathrm{~m} / \mathrm{s} \) at an angle of \( 60^{\circ} \) to the horizontal. Calculate the maximum height and the range covered by the stone. 13. A ball is projected horizontally from the edge of a platform at \( 12.0 \mathrm{~m} / \mathrm{s} \). If the platform is 8.0 m above the floor, what are the magnitude and direction of the ball's velocity as it hits the floor? 14. A particle is launched such that its maximum range is 26.4 m . What is the speed at which it is launched? 15. A rifle fires a bullet at \( 360 \mathrm{~m} / \mathrm{s} \). (a) At what angle must the rifle be positioned for the bullet to hit a target 242.4 m away at the same height as the rifle?(b) If gravitational force does not act on the bullet, how far above the target will the bullet pass maintaining the same angle? 16. A particle projected at an angle of \( \theta \) above the horizontal has a velocity of \( v=(16 i+5 j) \mathrm{m} / \mathrm{s} \) at time \( t=0.8 \mathrm{~s} \) after launching. (a) What is the maximum height of the particle? (b) What is the range of the particle? 17. A ball is kicked into the air. When it reaches the vertical height of 7.5 m , the velocity is measured to have a horizontal component of \( 10.4 \mathrm{~m} / \mathrm{s} \) and a vertical component of \( 3.7 \mathrm{~m} / \mathrm{s} \). Calculate the maximum height and horizontal distance, which the ball travels.

Two forces act at a point the magnitude of the two forces 6,8 newton and the meas f the included angle between them \( \theta \in\left[0, \frac{\pi}{2}[\right. \), then the magnitude of their resul ould be equal \( \qquad \) newton. 5 (b) 10 (c) 12 (d) 16