Question 5.C-A.63: A cube made up of a metal weighs 308 g in air and 260 g in w...

A cube made up of a metal weighs 308 g in air and 260 g in water but a cavity is present inside it. Find the volume of the cavity if the relative density of the metal is 11.

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(i) Find the weight of the cube in air (W_{1})  and in water (W_{2}) .

Find the apparent loss in the weight of the cube i.e., (W_{1} – W_{2})                  (1)

But (W_{1} – W_{2}) = upthrust acting on the cube

⇒          W_{1} – W_{2} = V. d_{water.}g                         (2)

From (2), find the volume of the cube (V_{1})

Find the relative density(d) of the metal from the given data.

Find the volume of the metal (V_{2}) from using the formula.

V_{2}=\frac{W_{1}}{d}

Now, the volume of the cavity = V_{1} – V_{2}.

(ii)  20 cm ^{3}

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