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Partially Inelastic Collision

The equation ...

Question

The equation of a gas is given by : $P V = A T + B T^{2}$ , where $P =$ pressure, $V =$ volume, $T =$ temperature. The dimensions of constant B are

[M L^{2} T^{- 4}]

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[M L^{2} T^{- 2} θ^{- 2}]

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[M L]

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[M L^{2} T^{- 2}]

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Solution

The correct option is B $[M L^{2} T^{- 2} θ^{- 2}]$
We know the dimension of P and V, using that dimension of PV
$[P V] = [M L^{2} T^{- 2}]$ ,
The dimension of PV will be equal to the remaining two, which are being added. Equating the dimension
$[A T] = [M L^{2} T^{- 2}]$
$[B T^{2}] = [M L^{2} T^{- 2}]$
$[B] = [M L^{2} T^{- 2} θ^{- 2}]$

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