Question

Write the dimensions of a and b in the relation f=a√x+ bt^2

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]

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Answer 2

Answer:

[a/b] = [M0 L−½ T2]

Step-by-step explanation:

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]