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Question

Two masses 8 kg and 12 kg are connected at the two ends of a light inextensible string that goes over a frictionless pulley. Find the acceleration of the masses, and the tension in the string when the masses are released.

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Solution

Given: The two masses are 8 kg and 12 kg respectively.

The free body diagram for the system is shown below.



The equation of motion can be written as,

T m 1 g= m 1 a (1)

m 2 gT= m 2 a(2)

Where, T is the tension in the string and a is the acceleration.

On adding equations (1) and (2), we get

T m 1 g+ m 2 gT= m 1 a+ m 2 a ( m 2 m 1 )g=( m 1 + m 2 )a a= ( m 1 + m 2 ) ( m 2 m 1 ) g

By substituting the given values in the above equation, we get

a= 128 12+8 ×10 = 4 20 ×10 =2 ms 2

Thus, the acceleration of the masses is 2 ms 2 .

By substituting the value of a in equation (2), we get

12×10T=12×2 T=12024 =96N

Thus, the tension in the string is 96N.


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