Grade 11Mechanics
find the dimensions of a and b if f = a root x +bt square .where f is force x is distance t is time
find the dimensions of a and b if f = a root x +bt square .
where f is force x is distance t is time
1 Answer
Arun
Approved Tutor Answer8 Years agof = 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]
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]
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