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Question

Two thin and light rods A and B are attached to a block of mass m with the help of a massless string as shown in the figure. Then identify the correct statement, if the angle between the rods is acute.


A
Both A and B experience compression
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B
Both A and B experience extension
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C
A experiences extension and B experiences compression
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D
B experiences extension and A experiences compression
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Solution

The correct option is C A experiences extension and B experiences compression
The tension in rods and string connecting the block is shown in figure given below.


F.B.D of block,


Let tension in the rods A and B be TA and TB respectively.
Applying equilibrium condition on block,
T=mg ....(i)
Applying equilibrium condition for the point at junction of both rods.
For vertical equilibrium,
TAsinθ=T=mg ...(ii)
For horizontal equilibrium,
Fx=0
TB+TAcosθ=0
TB=TAcosθ ...(ii)
From Eq.(i),
TB=mgsinθ×cosθ
TB=mgcotθ
Since θ is acute angle i.e cotθ will be positive and mg is itself a positive quantity, therefore TB comes to be negative.

Hence negative sign for TB(tension in rod B), indicates that rod B experiences compression. However the sign of tension in rod A is +ve, so it will experience extension.

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