(a) 8 (b) \( 8 \sqrt{2} \quad(c) 8 \sqrt{3} \quad(d) 12 \) (49) A uniform rod \( \overline{A B} \) of length 6 meters and weight \( 8 \mathrm{~kg} \cdot \mathrm{wt} \). is attached to a hinge fixed in a vertical wall at its end A the rod is kept horizontal by attaching it at a point C on the rod (where \( A C=4 \) meters) by a string which its other end is fixed at the point D on the wall above A exactly and at a distance 4 meters from it. Calculate the magnitude of the tension in the string and the reaction of the hinge.

must be the charge of a Figure \( 23-40 \) shows a section of a \( R=3.00 \mathrm{~cm} \), with a charge per unit length of \( \lambda=2.00 \times 10^{-8} \mathrm{C} / \mathrm{m} \). What is the magnitude \( E \) of the electric field at radial distance (a) \( r=R / 2.00 \) and (b) \( r=2.00 R \) ? (c) Graph \( E \) versus \( r \) forthe range \( r=0 \) to 2.00R.

10. The distance travelled by a free falling object varies directly to the square of the time taken. Given that an object dropped a distance of 19.6 m after 2 seconds, find the distance dropped after 5 seconds.

Example 10 Three coplanar forces of magnitudes \( F, 5,3 \) Newton act on a particle and the measure of the angle between the second the third force is \( 60^{\circ} \). Find the value of \( F \) if the forces are in equilibrium.

24. Let \( |\vec{A}|=150 N \) and the vector \( \vec{A} \) makes an angle of \( 60^{\circ} \) with the positive y axis. Let P be the scalar projection of \( \vec{A} \) on to the xz plane and it makes an angle of \( 30^{\circ} \) with the positive x axis. Express vector \( \vec{A} \) in terms of its rectangular \( (\mathrm{x}, \mathrm{y}, \mathrm{z}) \) components;

Describe the law of conservation of momentum as it pertains to a real-life scenario, and explain how it applies. Begin by identifying the real-life scenario. You may start your response with: - A real-life scenario pertaining to conservation of momentum is ... - In this scenario, the law of conservation of energy applies because . . .