The relation between force ' $F$ ' and density ' $\mathrm{d}$ ' is $\mathrm{F}=\frac{\mathrm{x}}{\sqrt{\mathrm{d}}}$. The dimensions of $\mathrm{x}$ areA) $\left[\mathrm{L}^{-1 / 2} \mathrm{M}^{3 / 2} \mathrm{~T}^{-2}\right]$B) $\left[\mathrm{L}^{-1 / 2} \mathrm{M}^{1 / 2} \mathrm{~T}^{-2}\right]$C) $\left[\mathrm{L}^{-1} \mathrm{M}^{3 / 2} \mathrm{~T}^{-2}\right]$D) $\left[\mathrm{L}^{-1} \mathrm{M}^{1 / 2} \mathrm{~T}^{-2}\right]$

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The relation between force ‘ $F$ ‘ and density ‘ $\mathrm{d}$ ‘ is $\mathrm{F}=\frac{\mathrm{x}}{\sqrt{\mathrm{d}}}$ . The dimensions of $\mathrm{x}$ are
A) $\left[\mathrm{L}^{-1 / 2} \mathrm{M}^{3 / 2} \mathrm{~T}^{-2}\right]$
B) $\left[\mathrm{L}^{-1 / 2} \mathrm{M}^{1 / 2} \mathrm{~T}^{-2}\right]$
C) $\left[\mathrm{L}^{-1} \mathrm{M}^{3 / 2} \mathrm{~T}^{-2}\right]$
D) $\left[\mathrm{L}^{-1} \mathrm{M}^{1 / 2} \mathrm{~T}^{-2}\right]$

Physics

The relation between force ‘ $F$ ‘ and density ‘ $\mathrm{d}$ ‘ is $\mathrm{F}=\frac{\mathrm{x}}{\sqrt{\mathrm{d}}}$ . The dimensions of $\mathrm{x}$ are
A) $\left[\mathrm{L}^{-1 / 2} \mathrm{M}^{3 / 2} \mathrm{~T}^{-2}\right]$
B) $\left[\mathrm{L}^{-1 / 2} \mathrm{M}^{1 / 2} \mathrm{~T}^{-2}\right]$
C) $\left[\mathrm{L}^{-1} \mathrm{M}^{3 / 2} \mathrm{~T}^{-2}\right]$
D) $\left[\mathrm{L}^{-1} \mathrm{M}^{1 / 2} \mathrm{~T}^{-2}\right]$

Correct option is A.

$\text { The dimensions of } \mathrm{x} \text { are }[\mathrm{x}]=[\mathrm{F}][\mathrm{d}]^{0.5}=\left[\mathrm{MLT}^{-2}\right]\left[\mathrm{ML}^{-3}\right]^{0.5}=\left[\mathrm{M}^{1.5} \mathrm{~L}^{-0.5} \mathrm{~T}^{-2}\right]$

i

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