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Question

Two blocks A and B each of equal masses m are related from the top of a smooth fixed wedge as shown in the figure. Fine the magnitude of the acceleration of the centre of mass of the two blocks.
983386_104e5f30dd3e490e91ca8da7dfa88684.png

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Solution

Letus consider incline surface of wedge as x-axis and y-axis respectively. We can write acceleration of blocks A and B.
¯aA=mgsin30o^i and ¯aB=mgsin30o^j
The acceleration of centre of mass of two blocks can be written as
¯acm=mA¯aA+mB¯aBmA+mB=mgsin30o^i+mgsin60o^jm+m
gsin30o^i+gsin60o^j2
g4^i+34^j1¯acm1=g2
1031219_983386_ans_fc9d46b66f624177932b7bdd70d3558f.png

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