# Find the tension in the string and accelerations of blocks A and B weighing 200N and 50N respectively,

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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. +1 vote
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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)

50 = 10.19a

a = 4.9m/sec

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

T = 75N.