A body weighs W 1 in a liquid of density d 1 and W 2 in a liquid of density d 2 - What is the weight in a liquid of density d 3 -A- W 3-W2d1-d3-W1d3-d2-d2-d1B- W 3- W 2 d 3- d 1- W 1 d 3- d 2- d 2- d 1C- W 3-W2d3-d1-W1d3-d2-d1-d2D- w 3-W 1d3-d1-W2d3-d2-d2-d1

The correct option is B W_1 = mg [ 1 d_1/D] = W[ 1 d_1/D] nbsp; nbsp; nbsp; nbsp; .........(a) Similarly, W_2 = mg [ 1 d_2/D] = W[ 1 d_2/D] ...

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Byju's Answer

Standard XII

Physics

Archimedes' Principle

A body weighs...

Question

A body weighs $W_{1}$ in a liquid of density $d_{1}$ and $W_{2}$ in a liquid of density $d_{2}$ . What is the weight in a liquid of density $d_{3}$ ?

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Solution

The correct option is B

$W_{1}$ = mg $[1 - \frac{d_{1}}{D}]$ = W $[1 - \frac{d_{1}}{D}]$ .........(a)

Similarly, $W_{2}$ = mg $[1 - \frac{d_{2}}{D}]$ = W $[1 - \frac{d_{2}}{D}]$ .........(b)

and $W_{3}$ = mg $[1 - \frac{d_{3}}{D}]$ = W $[1 - \frac{d_{3}}{D}]$ .........(c)

Using (a) , (b) & (c) we obtain

$W_{3}$ = $\frac{W_{2} (d_{3} - d_{1}) - W_{1} (d_{3} - d_{2})}{d_{2} - d_{1}}$

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