-->

Laws Of Motion

Question
CBSEENPH11016691

In the figure below, each mass is m. Find the tension T1 and T2.


Solution
Let a be the acceleration of the system.
The equation of motion of mass A is, 
mg space minus space straight T subscript 2 space equals space ma space space space space space space space... left parenthesis 1 right parenthesis space

The space equation space of space motion space of space mass space straight B space is comma space

mg space plus space straight T subscript 2 space minus space straight T subscript 1 equals space ma space space space space space... space left parenthesis 2 right parenthesis space

The space equation space of space moton space space of space mass space straight C space is comma space

straight T subscript 1 minus space mg space equals space ma space space space space space space space space space space space space space... space left parenthesis 3 right parenthesis space

Adding space equations space left parenthesis 1 right parenthesis comma space left parenthesis 2 right parenthesis space and space left parenthesis 3 right parenthesis comma space we space get

acceleration comma space straight a space equals space straight g divided by 3 space

From space equation space left parenthesis 1 right parenthesis comma space we space have

straight T subscript 2 space equals space mg space minus space ma space equals space mg space minus space straight m straight g over 3 space equals space 2 over 3 mg

From space equation space left parenthesis 3 right parenthesis comma space we space have

straight T subscript 1 space equals space mg space plus space ma space equals space mg space plus straight m straight g over 3 space equals space 4 over 3 mg