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Question

Two blocks A and B each of equal masses 'm' are released from the top of a smooth fixed wedge as shown in the figure. The magnitude of acceleration of the centre of mass of the two blocks is ___.

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Solution



Let us consider incline surfaces of wedge as x-axis and y-axis respectively. We can write accelerations of blocks A and B.
aA=mg sin 30^i and aB=mg sin 60^j
The acceleration of centre of mass of two blocks can be written as
aam=mAaA+mBaBmA+mB=mg sin 30^i+mg sin 60^jm+m
=g sin 30^i+mg sin 60^jm+m
=g4^i+3g4^j|aam|=g2

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