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Two blocks of masses m(1) and m(2) are c...

Two blocks of masses `m_(1)` and `m_(2)` are connected by massless threads. The pulleys are massless and smooth if `a_(1)` is the magnitude value of acceleration of `m_(1)` and `a_(2)` is the magnitude value of acceleration of `m_(2)` find the ratio of `a_(1)/a_(2)`

Text Solution

Verified by Experts

The correct Answer is:
4

From the figure,
`l_(1)+2l_(3)` = constant
Differentiating twice w.r.t. time t, we have
`a_(1)+2a_(3)=0`
Also, `l_(2)+(l_(2)-l_(3))` = constant
Differentiating twice w.r.t. time, we have
`2a_(2)-a_(3)=0`
`2a_(2)=a_(3)`
Substituting in eqn. (i)
`a_(1)+2(2a_(2))=0`
`a_(1)=-4a_(2)`
`a_(1)/a_(2)=4 ("in magnitude")`
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