Question

Write the dimensions of a/b in the relation f=ax+bt2

Answer 1

f = a√x + bt2, where [f] = [M L T −2], [x] = [L] and [t] = [T].

LHS is force. So both the terms on the RHS have the dimensions of force.

[f] = [a√x] = [bt2]

[f] = [a√x]
[M L T −2] = [a L½]
⇒ [a] = [M L½ T −2]

[f] = [bt2]
[M L T −2] = [b T2]
⇒ [b] = [M L T−4]

[a]/[b] = [M L½ T −2]/[M L T−4] = [M0 L−½ T2]

Therefore       [a/b] = [M0 L−½ T2]

Answer 2

F = [  M ¹ L¹ T⁻² ]

Now a = F / x                   x = L 

so , a = M¹  T⁻²

F = bt²

b= f / t² 

b = [ M¹ L¹ ]