Question

A solid cube of dimensions $50\,cm \times 50\,cm$ and weighing $25\,N$ placed on a table. Calculate the pressure exerted on the table.

Answer 1

Hint: We know that the pressure exerted is the force acting per unit area. Here, the weight of the cube acts as the force. The area on which it acts is the area of the base of the cube. Using these we can find the value of pressure.

Complete step by step solution:
It is given that a solid cube has a dimension $50\,cm \times 50\,cm$ .
So, the length of each side is $50\,cm$
Let the length of the side be represented as a.
So, $a = 50\,cm$
$ \Rightarrow a = 0.5\,\,m$
Weight of the solid cube is given as
$W = 25\,N$
We need to find the pressure exerted by this cube on the table.
We know that the pressure exerted is the force acting per unit area.
 $P = \dfrac{F}{A}$
Where P is the pressure, F is the force applied and A is the area.
In this question the weight of the cub is acting as the force. Hence we can write the value of force as
$F = 25\,N$
Now we need to find the area. The area on which this force acts is the area of the base of the cube.
The length of each side of the cube is $0.5\,m$
Hence the area of the base which is a square can be found by taking the square of length of side.
$ \Rightarrow A = a \times a$
On substituting the values, we get area as,
$ \Rightarrow A = 0.5 \times 0.5\,{m^2}$
$ \Rightarrow A = 0.25\,{m^2}$
 Now let us substitute the value of force and area in the equation for pressure.
$ \Rightarrow P = \dfrac{F}{A}$
$ \Rightarrow P = \dfrac{{25}}{{0.25}}$
$ \Rightarrow P = 100\,N/{m^2}$
$ \Rightarrow P = 100\,Pa$

This is the pressure exerted by the solid cube on the table.

Note: The pressure will vary inversely with the area. Since, we are asked to find the pressure due to a solid cube we will get the same value of pressure irrespective of the sides taken as base. If it was a rectangular block then the value of area for length and breadth as the base will be different from the value of breadth and height as the base. In our case since the value length and breadth and height is the same, we will get the same for any combination taken as base.