Two masses m and M ( > m ) are joined by a light string passing over a smooth light pulley. The centre of…

Two masses m and M (>m) are joined by a light string passing over a smooth light pulley. The centre of mass of the system moves with an acceleration


  1. gM-mM+m downward
  2. gM-mM+m2 downward
  3. gM-mM+m2 upward if M < m
  4. zero

Solution

a com = m 1 a 1 ¯ + m 2 a 2 ¯ m 1 + m 2

a com = 1 m+M [ M( M−m ) m+M - m( M−m ) m+M ]g

= 1 m+M [ ( M−m ) 2 m+M ]g= ( M−m M+m ) 2 g

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