Question

If force, length and time were the fundamental units, then the dimensional formula of mass would have been-

• A. $\text{F }\text{L}^{\text{-1}}\text{ }\text{T}^{2}$
• B. $\text{F L T}\text{ }^{\text{-2}}$
• C. $\text{F L }\text{T}^{\text{ -1}}$
• D. F

Answer 1

Answer: (A)

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

Answer 2

$Mass \propto F^{a}L^{b}T^{c}$

$M ^ { 1 } L ^ { 0 } T ^ { 0 } = \left[ M ^ { 1 } L ^ { 1 } T ^ { - 2 } \right] ^ { a } [ L ] ^ { b } [ T ] ^ { c }$ $M^{1}\text{ }\text{L}^{0}\text{ }\text{T}^{0}\ = \text{ }\text{M}^{a}\text{ }\text{L}^{a + b}\text{ T}\text{ }^{\text{-2a} + c}$

so a = 1 a = 1a + b = 0 Ž b = – 1

– 2a + c = 0 c = 2