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Earth's Gravitational Acceleration

Suppose a qua...

Question

Suppose a quantity x can be dimensionally represented in terms of M, L and T, that is, $[x] = M^{a} L^{b} T^{c}$ . The quantity mass
(a) can always be dimensionally represented in terms of L, T and x,
(b) can never be dimensionally represented in terms of L, T and x,
(c) may be represented in terms of L, T and x if a = 0,
(d) may be represented in terms of L, T and x if $a \neq 0$ .

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Solution

(d) may be represented in terms of L, T and x if $a \neq 0$

If a = 0, then we cannot represent mass dimensionally in terms of L, T and x, otherwise it can be represented in terms of L, T and x.

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Q. Suppose a quantity x can be dimensionally represented in terms of M, L and T, that is,

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