In an experiment to determine Young's modulus of a wire, the...

The formula for Young's modulus is given by $Y = \dfrac{4MgL}{\pi d^2 l}$.

Here, $4$, $g$, and $\pi$ are constants and do not contribute to the percentage error.

The maximum percentage error in $Y$ is given by the sum of the individual relative errors multiplied by their respective powers:

$\left(\dfrac{\Delta Y}{Y}\right) \times 100 = \left(\dfrac{\Delta M}{M}\right) \times 100 + \left(\dfrac{\Delta L}{L}\right) \times 100 + 2\left(\dfrac{\Delta d}{d}\right) \times 100 + \left(\dfrac{\Delta l}{l}\right) \times 100$

Substituting the given percentage errors:

\left(\dfrac{\Delta Y}{Y}\right) \times 100 = 1\% + 1.5\% + 2(3\%) + 2.5\%$<br><br>\left(\dfrac{\Delta Y}{Y}\right) \times 100 = 1\% + 1.5\% + 6\% + 2.5\% = 11\%$.

Answer: $11\%$