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.

Problem (2) \( A \) iniform ladder \( A B \) of weight 10 kg .w and 3 m length rests with its end \( A \) on a smooth horizomal noor and is end B on a smooth vertical wall. the ladder is kept in equilibritum by a rope tied to on of irs ends A. and irs other end is attached to a point on the hori=ontal plane vertically below B. if the ladder is inclined at \( +5^{\circ} \) to the horizontal, a man of weight 60 kg . w was ascending the ladder find the magnitude of the tension in the rope when the man is \( 2 m \) away from \( A \) \( \qquad \) \( \qquad \)

Sebuah mobil bermassa 1200 kg bergerak dengan kecepatan \( 20 \mathrm{~m} / \mathrm{s} \). Mobil tersebut kemudian direm hingga berhenti setelah menempuh jarak 50 meter. Berapakah gaya pengereman yang bekerja pada mobil tersebut?

Problem (1) uniform bar \( A B \) of mass 40 kg and 8 m length is fixed in a vertical plane by two strings \( A D \) Id \( B H \), and a body of mass 60 kg is humg at a point \( C \) on \( A B \) so the bar became in an quilibrium state horizontally, and \( m(\angle D A B)=120^{\circ}, m(<H B A)=150^{\circ} \). find the magnitude fine tension in each of the strings and the length \( \overline{A C} \). Answer.

La cantidad de un material radiactivo disminuye a la mitad cada 10 años. Si comenzamos con 80 gramos, ¿cuánto quedará después de 30 años?

14. A train moving at an average speed of \( 72 \mathrm{~km} / \mathrm{h} \) takes 15 seconds to completely cross a bridge that is 80 metres long (a) Express \( 72 \mathrm{~km} / \mathrm{h} \) in metres per second (b) Find the length of the train in metres ( 2 mk )