# Two particles A and B, of mass 3·1 kg and 1·8 kg respectively, connected by a light inextensible string passing over a fixed smooth pulley. Initially, B is held at rest with the string taut. It...

Two particles A and B, of mass 3·1 kg and 1·8 kg respectively, connected by a light inextensible string passing over a fixed smooth pulley. Initially, B is held at rest with the string taut. It is then released.

Calculate the magnitude of the acceleration of A and the tension in the string.

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The situation is attached in the image

Using the Newton second law of motion to particle A,

`darrF=ma`

`3.1g-T =3.1a` --------------(1)

Using the Newton second law of motion to particle B,

`uarrT-1.8g =1.8a` -----------------(2)

(1)+(2)

`g(3.1-1.8)=a(3.1+1.8)`

`a=2.60m/s^2`

(1)/(2)  `(3.1g-T)/(T-1.8g) = (3.1/1.8)`

`1.8(3.1g-T)=3.1(T-1.8g)`

`T=22.34N.`

So acceleration and tension of the string is `2.6m/s^2` and `22.34N` respectively.

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