Pressure depends on distance as, P= αβexp-αZkθ Where α,β are constants, z is distance , k is Boltzmann constant and θ is temperature. The dimensions of β are :
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a
[M0L0T0]
b
[M-1L-1T-1]
c
[M0L2 T0]
d
[M-1 L-1 T2 ]
answer is C.
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Detailed Solution
The quantity in exponential must be dimensionless soαZkθ=M0L0T0⇒[α]=[MLT-2 ] Also [P] = αβ Hence [β] = [αP-1] =MLT-2 M-1LT2=[M0L2T0 ]