Question

An object of weight $3\times {10}^{5}N$ has a volume of $60m^3$. Select the correct option based on the given information. Assume $g=10m{s}^{-2}$.
(i) Relative density of the object is 5.
(ii) Relative density of the object is 0.5.
(iii)The object will float on water.
(iv)The object will sink in water.

• A. (i) and (iii)
• B. (i) and (iv)
• C. (ii) and (iii)
• D. (ii) and (iv)

Answer 1

The correct option is C (ii) and (iii)

Weight of the object, $W=3\times {10}^{5}N$
Volume of the object, $V=60m^3$
$g=10m{s}^{-2}$
Mass of the object $=\frac{W}{g}=\frac{(3\times {10}^{5}N)}{\left(10m{s}^{-2}\right)}=3\times {10}^{4}kg$
Density of the object,
$D=\frac{\left(massoftheobject\right)}{\left(volumeoftheobject\right)}$
$D=\frac{(3\times {10}^{4}kg)}{\left(60m^3\right)}=500kg{m}^{-3}$
Now, relative density of the object,
$D_r=\frac{\left(Densityoftheobject\right)}{\left(Densityofwater\right)}$
$\Rightarrow D_r=$$\frac{500}{1000}$
$D_r=0.5$
Since, the relative density of the object is less than water, it will float on water. Hence, statements (ii) and (iii) are correct.