Question

A cubical block of wood of length $5\,cm$ is kept on a table top. The density of the block is $800\,kg{m^{ - 2}}$ and $g = 9.8\,m{s^{ - 2}}$ . Find the pressure exerted by the wooden block on the table top.

Answer 1

Hint:Here first we have to find the mass from the density mass and volume relationship. Then we can find the pressure using the mass, acceleration due to gravity and area.Density is a per-volume indicator of mass. The average density of an object is proportional to its total mass divided by its total height. An object made from a more dense material (such as iron) would have less volume than an object of equal mass made from a less dense substance (such as water).

Complete step by step answer:
Given: Length, $l = 5\,cm$, Density, $d = 800\,kg{m^{ - 2}}$, Acceleration due to gravity, $g = 9.8\,m{s^{ - 2}}$
We know that,
Density,
$
d = \dfrac{{{\text{mass}}}}{{{\text{volume}}}} \\
\Rightarrow 800 = \dfrac{m}{{125\,c{m^3}}} \\
\Rightarrow 800 = \dfrac{m}{{125 \times {{10}^{ - 6}}\,{m^3}}} \\
\Rightarrow m = 0.1\,kg \\
$
Now, pressure,
$
P = \dfrac{{{\text{Force}}}}{{{\text{Area}}}} \\
\Rightarrow P = \dfrac{{mg}}{A} \\
\Rightarrow P = \dfrac{{0.1 \times 9.8}}{{0.05 \times 0.05}} \\
\Rightarrow P = 292\,N{m^{ - 2}} \\
\therefore P = 292\,Pa \\
$
Hence, the pressure exerted on the table top is $292\,Pa$.

Additional information:
When a net force is applied, mass is both a function of a human body and a measure of its resistance to acceleration (a change in its state of motion). The mass of an object therefore determines the force of its gravitational pull against other bodies. A kilogram is the fundamental SI unit of mass.

Volume is the amount of three-dimensional space surrounded by a closed membrane, for example, the space that a material (solid, liquid, gas, or plasma) or form occupies or comprises. Volume is also numerically quantified using the cubic metre, the SI derived unit.The physical force exerted on an object is known as pressure. Per unit field, the force applied is perpendicular to the surface of objects.

Note:Here we have to see whether the standard units are given or not. If not given we have to convert them to standard units otherwise the answer would be wrong by a factor of ten or hundred. Also, we have to use the acceleration due to gravity when gravity is not given.