An object A, of mass of 4 kg, on a rough horizontal table connected by a light inextensible string passing over a smooth light pulley, fixed at the edge of the table, to an object B, of mass 6 kg, hanging freely. The coefficient of friction between the object and the table is 0•3. Initially, the system is held at rest with the string taut. It is then released.

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

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Forces acting on each objects are shown in the attached figure.

For object B(6 kg):

`mg-T=ma`

`rArr 6*9.81-T=6a`

`rArr 58.86-T=6a`

`rArr T=58.86-6a` ..........(i)

For object A (4 kg) there is no vertical acceleration. So, `R=4g=4*9.81=39.24 N`

In the horizontal direction the object is accelerating to the right, so the equation is `T - muR = 4a`

Here, `mu=0.3` . Substituting T from equation (i) and plugging in the values of `mu` and` R` we get:

`58.86-6a-0.3*39.24=4a`

`rArr 10a=58.86-11.772`

`rArr a=47.088/10=4.708` m/s^2

Hence, `T=58.86-6*4.708=30.612 N`

Therefore, the magnitude of the acceleration of A is **4.708 m/s^2** and the tension in the string is **30.612 N**.

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