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In the system shown in fig., m(A)=4m, m(...

In the system shown in fig., `m_(A)=4m`, `m_(B)=3m`, and `m_(c)=8m`. Friction is absent everywhere. String is inextensible and light. If the system is released from rest, then

Acceleration of Block B is

Text Solution

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The correct Answer is:
Vertical acceleration of `A=a=6.25ms^(-2)` (downwards) ; Horizontal acceleration of `A=c=1.25 ms^(-2)` (rightward) ; Acceleration of `B=(a-c)=5.00 ms^(-2) (leftward)` ; Acceleration of `C=c=1.25ms^(-2)` (rightward).
Let verically downward component of acceleration of A be a and let acceleration of C be c (rightward).
Then horizontal component of acceleration of A is c (rightward) and acceleration of B, relative to C is a (leftward). Hence, resultant acceleration of B is ,`(a-c)` leftward.
Now considering free body diagrams.

For block A,
`H=2c` ...(i)
`2g-T=2a` ..(ii)
For horizontal forces on block B,
`T=1.5(a-c)`...(iii)
For horizontal force on block C,
`T-H=4C` ..(iv)
From above equations,
`A=6.25 ms^(-2) and c=1.25 ms^(-2)`
Vertical acceleration of `A=a=6.25ms^(-2)` (downwards)
Horizontal acceleration of `A=c=1.25 ms^(-2)` (rightward)
Acceleration of `B=(a-c)=5.00 ms^(-2) ("leftward")`
Acceleration of `C=c=1.25ms^(-2)` (rightward).
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