Question

A force f is given by f =at+bt2,where t is time.what are the dimension of a and b

Answer 1

As you have Force on Left Hand Side, the right hand side quantities also represent force....so at and bt^2 represent force.....  

but dimensional formula of force is  

Force: M1 L1 T(-2)  

so, dimensional formula of at and bt^2 is also M1 L1 T(-2)  

Means, [aT] = M1L1T(-2)  

SO, [a] = (M1 L1 T^-2)/T  

so [a] = M1 L1 T -3  

Same way for b,  

bt^2= force  

so b= force/t2 = m1 l1 t (-4)...  

Answer 2

Answer:

a=M^1L^1T^-3

b=M^1L^1T^-4

Explanation:

concept- dimensional equation LHS = RHS

f=M^1L^1T^-2]

f =at+bt2,

f=at

M^1L^1T^-2]=a[T]

a=M^1L^1T^-3

f=bt2

M^1L^1T^-2= b[T]^2

b=M^1L^1T^-4

#SPJ2