Question

A brick has dimensions of 3 cm  4 cm  9 cm. It is placed on plane horizontal surface in different orientations. What is the

ratio of maximum and minimum pressure exerted by the brick on the surface ?​

Answer 1

Answer:

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Answer 2

Given:

A brick has dimensions of 3 cm × 4 cm × 9 cm. It is placed on plane horizontal surface in different orientations.

To Find:

What is the ratio of maximum and minimum pressure exerted by the brick on the surface ?​

Solution:

Let weight of brick is given below:

Weight of brick = W

Length of brick = L = 9 cm

Breadth of brick = B = 4 cm

Height of brick = H = 3 cm

Surface area of brick have different value of different face:

Maximum surface area  $\mathbf{=A_{max}= 9\times 4=36 \ cm^{2}}$

Minimum surface area  $\mathbf{=A_{min}= 3\times 4=12 \ cm^{2}}$

We know that pressure exerted by force on minimum area has maximum value. While  pressure exerted by force on maximum area has minimum value:

We know the formula of pressure:

$\mathbf{Pressure=\dfrac{Force}{Area}}$

Now ratio of maximum pressure to minimum pressure is :

$\mathbf{\dfrac{P_{max}}{P_{min}}=\dfrac{\dfrac{W}{A_{min}}}{\dfrac{W}{A_{max}}}}$

On simplify:

$\mathbf{\dfrac{P_{max}}{P_{min}}=\dfrac{A_{max}}{A_{min}}}$

$\mathbf{\dfrac{P_{max}}{P_{min}}=\dfrac{36}{12}}$

$\mathbf{\dfrac{P_{max}}{P_{min}}=3}$

Means ratio of maximum pressure to minimum pressure is 3.