1.) Understanding the contractile response of an animal skeletal system is impor

Question

1.) Understanding the contractile response of an animal skeletal system is important in bio-mechanical studies. Towards this end, the studies have measured velocity-force data and modeled it using the following equation.

v=((F*a)/(F+b)) (1+ 1/(exp(-k(F-CF0))

Where v is velocity, F is applied force, and Fo is measured force. The model has four constant parameters - a, b, C, and k.

If M is used to represent dimension of mass, t for dimension of time, and L for dimension of length, choose the correct option below by applying the principle of dimensional homogeneity.

Explanation / Answer

Only homogeneous quanties are added => Dimensions of F = Dimensions of b =>[F] =[b]

=> [b] =[MLt^-2] ---------------> Option b is wrong

[F]*[a]/[F] = [v] ( since (1+ 1/(exp(-k(F-CF0) is dimensionless)

=> [a]= [v] =[L/t] ----------------> Option a is correct

=> final answer is A

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