Q121 / 160 · AP EAMCET 2023 (18 May Shift 1) · Physics

A certain physical quantity is calculated from the formula $\frac{\pi}{3}\left(a^2-b^2\right) h d$, where $a, b$ and $h$ are all lengths and $d$ is density. The physical quantity being calculated is

  • A
    velocity
  • B
    volume
  • Correct answer
    C
    mass
  • D
    acceleration

Solution

$\frac{\pi}{3}\left(a^2-b^2\right)$ hd ...(1) a, b, h has length "l" so there unit is $\mathrm{m}(\mathrm{L})$ $\mathrm{d}=$ density $=\frac{\text { Mass }}{\text { volume }}=\frac{\mathrm{kg}}{\mathrm{m}^3}=\frac{\mathrm{M}}{\mathrm{L}^3}$ $\frac{\pi}{3}$ has no dimensions from equation (1) Now, $\left(\mathrm{L}^2-\mathrm{L}^2\right) \frac{\mathrm{M}}{\mathrm{L}^3}(\mathrm{~L})$ $\frac{\mathrm{L}^3 \mathrm{M}}{\mathrm{L}^3}=\mathrm{M} \Rightarrow$ Mass

Hence, the correct answer is option: 'C'.

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