The pressure on a square plate is measured by measuring the force on the plate and the length of the sides of the plate. If the maximum error in the measurement of force and length are respectively 4% and 2%, The maximum error in the measurement of pressure is

The correct option is 8%.

To find the maximum error in the measurement of pressure, we first express pressure in terms of the measured quantities: force and length.

Pressure ($P$) is defined as the force ($F$) applied per unit area ($A$):
$P=\frac{F}{A}$
For a square plate with side length $L$, the area is:
$A=L^2$
Substituting the expression for area into the pressure formula gives:
$P=\frac{F}{L^2}$

By the rule of propagation of errors, the maximum relative error in a calculated quantity is the sum of the relative errors of its independent factors multiplied by their respective powers:
$\frac{\Delta P}{P}=\frac{\Delta F}{F}+2·\frac{\Delta L}{L}$

Multiplying by 100 to convert this into percentage error, we get:
$\left(\frac{\Delta P}{P}\times 100\right)=\left(\frac{\Delta F}{F}\times 100\right)+2·\left(\frac{\Delta L}{L}\times 100\right)$

We are given:
- Maximum error in force measurement = $4\%$
- Maximum error in length measurement = $2\%$

Substituting these percentage error values into the equation:
$\text{Maximum error in pressure}=4\%+2·(2\%)$
$\text{Maximum error in pressure}=4\%+4\%=8\%$