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Problem Solving

Blocks A and ...

Question

Blocks A and B are connected as shown in figure. Find the relation between acceleration of block A and B.

A

a_{A} = 2 a_{B}

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B

a_{B} = 2 a_{A}

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C

a_{A} = 4 a_{B}

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D

a_{B} = 4 a_{A}

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Solution

The correct option is A $a_{B} = 2 a_{A}$
To solve these kind of constraint relation problem, I will tell you a trick.
Consider block and tension as a system.
Now tension in the string is internal force, then
$\sum T_{i} a_{i} = 0$
Work done by all internal forces = $0$
Differentiating
$\sum T_{i} a_{i} = 0$
Let acc. of $2 M$ mass= $a_{B}$
and acc. of M mass= $a_{A}$
$\sum T_{i} a_{i} = 0$
$T a_{B} - T a_{A} = 0$
$a_{B} = 2 a_{A}$
$∴ O p t i o n B$

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