Units & Dimensions

JEE Main level, single correct, medium

97 of 149

Question 97 of 149

If velocity [V]\left[V\right] time [T]\left[T\right] and force [F]\left[F\right] are chosen as the base quantities, the dimensions of the mass will be :

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Answer: (D) [FTV−1]\left[FT{V}^{-1}\right]

[M]1=[V]a[T]b[F]c[M{]}^{1}=[V{]}^{a}[T{]}^{b}[F{]}^{c}
[M]1=[LT−1]a[T]b[MLT−2]c[M{]}^{1}={\left[L{T}^{-1}\right]}^{a}[T{]}^{b}{\left[ML{T}^{-2}\right]}^{c}
[M]1=[M]c[L]a+c[T]−a+b−2c[M{]}^{1}=[M{]}^{c}[L{]}^{a+c}[T{]}^{-a+b-2c}
Thus,
c=1,a+c=0andb−a−2c=0⇒a=−1⇒b=−1+2=1\begin{matrix}c=1, & a+c=0\text{and} & b-a-2c=0 \\ & \Rightarrow a=-1 & \Rightarrow b=-1+2=1\end{matrix}
Thus, [M]=[V]−1[T]1[F]1[M]=[V{]}^{-1}[T{]}^{1}[F{]}^{1}

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