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Question: If force [F], length [L] and time [T] are presumed to be the fundamental units, then the dimensional...

If force [F], length [L] and time [T] are presumed to be the fundamental units, then the dimensional formula of mass will be –

A

F L-1 T2\text{F }\text{L}^{\text{-1}}\text{ }\text{T}^{2}

B

 F L-1 T -2\text{ F }\text{L}^{\text{-1}}\text{ }\text{T}^{\text{ -2}}

C

F L-1 T -1\text{F }\text{L}^{\text{-1}}\text{ }\text{T}^{\text{ -1}}

D

F L

Answer

F L-1 T2\text{F }\text{L}^{\text{-1}}\text{ }\text{T}^{2}

Explanation

Solution

M1 L0 T0 = [F]a [L]b [T]cM^{1}\text{ }\text{L}^{0}\text{ }\text{T}^{0}\ = \ \lbrack F\rbrack^{a}\ \lbrack L\rbrack^{b}\ \lbrack T\rbrack^{c}

orM1 L0 T0 = [M L T-2]a [L]b [T]cM^{1}\text{ }\text{L}^{0}\text{ }\text{T}^{0}\ = \ \lbrack\text{M L }\text{T}^{\text{-2}}\rbrack^{a}\ \lbrack L\rbrack^{b}\ \lbrack T\rbrack^{c}or

M1 L0 T0 = Ma La+b T-2a + cM^{1}\text{ }\text{L}^{0}\text{ }\text{T}^{0}\ = \text{ }\text{M}^{a}\text{ }\text{L}^{a + b}\text{ }\text{T}^{\text{-2a } + \text{ c}}

̃ a = 1

a + b = 0 ̃ b = –1

–2a + c = 0 ̃ c = 2