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String tension in case of pulley with mass

  1. In case of a massless string around a massless pulley , tension on either side of the pulley has to be the same. But when the pulley has mass, we consider tensions to be different on each side. Now i got a solution from someone that since pulley has mass it now needs torque to rotate so the tensions cant be same. but what about the string?? the string is massless so wont it have infinite acceleration?
  2. pulley-spring-systemthe diagram is in the file attached. this is a question of simple harmonic oscillation in which time period has been asked. It can be easily done by energy conservation but i also wanted to know how t can be done by analysing the forces method. what will be the tension in the string?

Asked Vasudha Bhandari

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