Two rods of same mass and same length l_o but having different coefficient of expansions a and 3a are joined at P (see figure). System is placed on frictionless surface. If temperature of whole system is changed by DT, the displacement of junction point is

l_{0} α Δ T

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2 l_{0} α Δ T

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\frac{l_{0} α Δ T}{2}

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\frac{3}{4} l_{0} α Δ T

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Solution

The correct option is C $\frac{l_{0} α Δ T}{2}$
Net force on the system is zero hence displacement of the centre of mass of the system will be zero. Let x be the shift in P, then
$m (\frac{l_{0}}{2} (1 + α Δ T) + x) = m (\frac{l_{0}}{2} (1 + 3 α Δ T) - x) \Rightarrow x = \frac{l_{0} α Δ T}{2} ∴ (c)$

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Similar questions

Q. Two rods of same mass and same length

l_{0}

but having different coefficient of expansions

α

and

3 α

are joined at P (see figure). System is placed on frictionless surface. If temperature of whole system is changed by

△ T,

the displacement of junction point is

Two rods of same mass and same length $l_{0}$ but having different coefficient of expansions $α$ and $3 α$ are joined at P(see figure). System is placed on frictionless surface. If temperature of whole system is changed by $Δ T$ , the displacement of junction point is