Q126 / 160 · AP EAMCET 2020 (22 Sep Shift 2) · Physics

Find the apparent weight of a metallic block of density $5 \mathrm{~g} \mathrm{~cm}^{-3}$ and dimensions $5 \mathrm{~cm} \times 5 \mathrm{~cm} \times 5 \mathrm{~cm}$, in water.

  • A
    $5 \times 5 \times 5 \times 5 \mathrm{gf}$
  • B
    $4 \times 4 \times 4 \times 4 \mathrm{gf}$
  • C
    $5 \times 4 \times 4 \times 4 \mathrm{gf}$
  • Correct answer
    D
    $4 \times 5 \times 5 \times 5 \mathrm{gf}$

Solution

Density of metallic block, $$ \rho=5 \mathrm{~g} \mathrm{~cm}^{-3} $$ Volume of block, $$ V=5 \mathrm{~cm} \times 5 \mathrm{~cm} \times 5 \mathrm{~cm} $$ Upthrust force on the metallic block in water, $$ \begin{array}{rlr} F_1 & =m \cdot g & \\ & =\rho_w V \times g & {\left[\rho_w=1 \mathrm{~g} \mathrm{~cm}^{-3}\right]} \\ & =V g=5 \times 5 \times 5 \times g & \\ & =5 \times 5 \times 5 g f & \end{array} $$ $\therefore$ Apparent weight $=$ Weight of block - Upthrust force $$ \begin{aligned} & =m g-5 \times 5 \times 5 g f \\ & =(m-5 \times 5 \times 5) g f \\ & =(\rho V-5 \times 5 \times 5) g f \\ & =(5 \times 5 \times 5 \times 5-5 \times 5 \times 5) g f \\ & =5 \times 5 \times 5(5-1) g f \\ & =5 \times 5 \times 5 \times 4 g f \end{aligned} $$

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

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