A) \[[L{{T}^{-2}}],\,[L]\] and \[[T]\]
B) \[[{{L}^{2}}],\,[T]\] and \[[L{{T}^{2}}]\]
C) \[[L{{T}^{2}}],\,[LT]\] and \[[L]\]
D) \[[L],\,[LT]\] and \[[{{T}^{2}}]\]
Correct Answer: A
Solution :
Key Idea: According to principle of homogeneity of dimensions, the dimensions of all the terms in a physical expression should be same. The given expression is \[v=at+\frac{b}{t+c}\] From principle of homogeneity [a] [t] = [v] \[[a]=\frac{[v]}{[t]}=\frac{[L{{T}^{-1}}]}{[T]}=[L{{T}^{-2}}]\] Similarly, \[[c]=[t]=[T]\] Further, \[\frac{[b]}{[t+c]}=[v]\] or [b] = [v] [t + c] or \[[b]\,=[L{{T}^{-}}]\,[T]\,=[L]\] Note: If a physical quantity depends on more than three factors, then relation among them cannot be established because we can have only three equations by equalizing the powers of M, L and T.
You need to login to perform this action.
You will be redirected in
3 sec
