What is tension in strings?

You can do this questions by balancing the equation of force for the given bodies. For question 1, there are two forces acting on mass m - Downward force due to gravity = mg and upward force T which is tension in the string. The total force is zero. So we get

T = mg

Similarly in the second question. First equate the forces for the lower object,

T2 = mg

for the upper object the equation would be

T2 + mg = T1

Replace the value of T2, you will get T1

T1 = 2mg