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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