Let's assume that the block is descending downward, and we'll choose the upward direction as positive. The forces acting on the block are the tension force (T) in the string pulling upward and the force due to gravity (mg) pulling downward. The net force on the block is equal to its mass (M) multiplied by its acceleration (a).
Using Newton's second law, we have:
Net force = ma
T - mg = Ma,
Now, let's consider the mass of the string below point P. Since the string is inextensible, the tension in the string above and below point P is the same. Therefore, the tension force (T) in the string is acting on both the block of mass M and the string of mass M. So we can rewrite the equation as:-
T - Mg = Ma
We want to solve for the tension force (T), so we rearrange the equation:-
T = Ma + Mg
T = M(a + g)
where g is the acceleration due to gravity (approximately 9.8 m/s^2).
Thus, the tension in the string is T = M(a + g).
