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Find the tension in the string and accelerations of blocks A and B weighing 200N and 50N respectively, connected by a string and frictionless and weightless pulleys as shown in fig.

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Given Data, 

Weight of block A = 200N 

Weight of block B = 50N 

As the pulley is smooth, the tension in the string will be same throughout 

Let, T = Tension in the string a = Acceleration of block B 

Then acceleration of block A will be equal to half the acceleration of block 

B. Acceleration of block A = a/2 ...(i) 

As the weight of block is more than the weight of block B, the block A will move downwards whereas the block B will move upwards.

Consider the motion of block B,

Net force = T – 50 ...(ii) 

Since Net force, F = ma 

T – 50 = (50/9.81) a 

T – 50 = 5.1a ...(iii) 

Consider the motion of block A, 

Net force = 200– 2T ...(iv) 

Since Net force, F = ma 

200– 2T = (200/9.81)(a/2) 

200– 2T = 10.19a 

100 – T = 5.1a ........(v) 

Add equation (3) and (5) 

50 = 10.19a 

a = 4.9m/sec

Putting the value of a in equation (5) we get 

T = 75N.

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