JEE Main 2022 Physics question

Consider the efficiency of carnot's engine is given by , where and are constants. If T is temperature, k is Boltzmann constant, is angular displacement and x has the dimensions of length. Then, choose the incorrect option

(1)Dimensions of is same as that of force.
(2)Dimensions of is same as that of energy.
(3)Dimensions of is same as that of .
(4)Dimensions of is same as that of .Correct

Answer: (4)

Solution

The argument is dimensionless, so = [kT/x] = [Energy]/[Length] = , the dimension of force, so (1) is correct. Since and are dimensionless, , so $[α ]

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Question ID VK-034626