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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 g−T= 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 g−T= 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= 12−8 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 12×10−T=12×2 T=120−24 =96 N Thus, the tension in the string is 96 N.

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