The period of a body under SHM is presented b | vedclass

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(A) The dimensional formula for the given quantities are:$T = [T^1]$$P = [M^1 L^{-1} T^{-2}]$$D = [M^1 L^{-3} T^0]$$S = [M^1 L^0 T^{-2}]$Substituting

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$ - \frac{3}{2}, \frac{1}{2}, 1$

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(A) The dimensional formula for the given quantities are:$T = [T^1]$$P = [M^1 L^{-1} T^{-2}]$$D = [M^1 L^{-3} T^0]$$S = [M^1 L^0 T^{-2}]$Substituting these into the equation $T = P^a D^b S^c$:$[M^0 L^0 T^1] = [M^1 L^{-1} T^{-2}]^a [M^1 L^{-3}]^b [M^1 T^{-2}]^c$$[M^0 L^0 T^1] = M^{a+b+c} L^{-a-3b} T^{-2a-2c}$Comparing the powers of $M, L,$ and $T$ on both sides:$a + b + c = 0$ $(1)$$-a - 3b = 0 \implies a = -3b$ $(2)$$-2a - 2c = 1 \implies a + c = -1/2$ $(3)$From $(2)$,substitute $a = -3b$ into $(1)$:$-3b + b + c = 0 \implies c = 2b$Substitute $a = -3b$ and $c = 2b$ into $(3)$:$-3b + 2b = -1/2 \implies -b = -1/2 \implies b = 1/2$Then $a = -3(1/2) = -3/2$ and $c = 2(1/2) = 1$.Thus,the values are $a = -3/2, b = 1/2, c = 1$.

The period of a body under $SHM$ is presented by $T = P^a D^b S^c$; where $P$ is pressure,$D$ is density,and $S$ is surface tension. The values of $a, b,$ and $c$ are:

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