  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.

Solution

The correct option is The given system of two masses and a pulley can be represented as shown in the following figure: Smaller mass, m1=8 kg Larger mass, m2=12 kg Tension in the string = T Mass m2, owing to its weight, moves downward with acceleration a, and mass m1 moves upward. Applying Newton's second law of motion to the system of each mass: For mass m1: The equation of motion can be written as: T−m1g=m1a ..........(i) For mass m2: The equation of motion can be written as: m2g−T=m2a ........(ii) Adding equations (i) and (ii), we get: (m2−m1)g=(m1+m2)a∴ a=(m2−m1m1+m2)g…(iii)=(12−812+8)×10=420×10=2 m/s2 Therefore, the acceleration of the masses is 2 m/s2. Substituting the value of a in equation (ii), we get: m2g−T=m2(m2−m1m1+m2)g⇒12×10−T=12×2⇒T=96 N Therefore, the tension in the string is 96 N PhysicsNCERT TextbookStandard XI

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