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The torque produced by a force acting on a lever arm can be given by the formula T = k F r^a , where F is the force, r is the length of the lever arm, and k is a dimensionless constant. Using dimensional analysis, the value of the exponent a is found to be:

Option: 1


Option: 2


Option: 3


Option: 4


Answers (1)


The torque can be expressed in terms of force, length and time as T = F \times r , which has dimensions of ML^2T^{-2} . Using dimensional analysis, we can write T = k F r^a, where k is a dimensionless constant and a is the unknown exponent. Equating the dimensions on both sides, we get ML^2T^{-2} = [k] M^1L^1T^{-2}[F]^1[L]^a . Equating the dimensions of force and length, we get a+1=1, which gives a=0. Therefore, the value of a is 1.

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Shailly goel

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