Question

A force is given by F= at+bt^2, where t is time. What are the dimensions of a & b?

Answer 1

according to dimension rule
dimension of at=dimension of F
so, dimension of a =dimension of F/t
=MLT^-3
in this way dimension of b=MLT^-4

Answer 2

Answer:

MLT^-4

Explanation:

Since, the force is on the left hand side, therefore the right hand side quantities also represent force.  Thus, both at and bt² represent force.  

Dimensional formula of force -  M1 L1 T(-2)  

Dimensional formula of at and bt² will also be M1 L1 T(-2)  

Means, [aT] = M1L1T(-2)  

= [a] = (M1 L1 T-²)/T  

= [a] = M1 L1 T-³  

Similarly for b,  

force = bt²

so b= force/t2

= MLT^-4