1-) two blocks of mass 3.so kg and 8.00 kg are connected by a massless string that passes over a
frictionless pulley. the inclines are frictionless. find;

(a) the magnitude of the acceleration of each block and

(b) the tension in the string.

The magnitude of the acceleration of each block is, a = 2.56 m/s²

The tension in the string is, T = 43.05 N

Explanation:

Given data,

The larger block of mass, M = 8.00 kg

The smaller block of mass, m = 3.50 kg

The formula for Atwood machine is,

                     Ma = Mg - T

                      ma = T - mg

Adding those equations,

                    a (M + m) = g ( M - m)

                        a = (M + m) / ( M - m)

Substituting the values,

                        a = (8 + 3.5) / (8 - 3.5)

                           = 2.56 m/s²

The magnitude of the acceleration of each block is, a = 2.56 m/s²

The tension in the string,

                       T = m(a + g)

                           = 3.5 ( 2.56 + 9.8)

                            = 43.05 N

The tension in the string is, T = 43.05 N