Tension in the string and acceleration of body:

The two bodies weighing 300N and 450N are hung to two ends of the rope passing over an ideal pulley as shown in the figure given below. With what acceleration will heavier body come down? What is tension in the string?

Sol: As string is light, inextensible and frictionless, so tension in the string on both the side is equal to T, let acceleration of both block is 'a'.

Let block weighting 450N moves down,

Consider motion of 450N block, Apply relation, F = ma

450 - T = (450/9.81) a

450 - T = 45.87a                                                                                                                                 ...(i)

Consider motion of 300N block,

Apply the relation, F = ma

T - 300 = (300/9.81) a

T - 300 = 30.58a                                                                                                                               ...(ii)

Add equation (1) and (2)

150 = 76.45a

a = 1.962m/sec²                                                                                              .......ANS

Putting value of a in equation (i),

T = 360N                                                                           .......ANS