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Question

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


A
FLT
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B
F1L1T2
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C
F2L2T2
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D
F1L1T2
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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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