Question

# If force $$F$$, length $$L$$ and time $$T$$ are chosen as fundamental quantities, then the dimensional formula for mass is:

A
FLT
B
F1L1T2
C
F2L2T2
D
F1L1T2

Solution

## The correct option is D $${ F }^{ 1 }{ L }^{ -1 }{ T }^{ 2 }$$Mass $$=M^{1}L^{0}T^{0}=F^{\alpha}L^{\beta}T^{\gamma}$$$$M^{1}L^{0}T^{0}=(MLT^{2})^{\alpha}(L)^{\beta}(T)^{\gamma}$$$$M^{1}L^{0}T^{0}=M^{\alpha}L^{\alpha+\beta}T^{-2\alpha+\gamma}$$$$\alpha=1,\alpha+\beta=0 \Rightarrow \beta=-1$$$$-2 \alpha + \gamma=0$$$$\Rightarrow \gamma =2$$$$\Rightarrow Mass = F^{1}L^{-1}T^{2}$$Physics

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