A steel wire of cross-sectional area 4 cm ^ 2 has elastic limit of...

Given, $Y = 2. 2 \times {10}^{8}ms^{- 2}$

Area of cross-section of steel wire,

$A = 4{cm}^{2} = 4 \times {10}^{- 4}m^{2}$

Mass of elevator, $m = 1000kg$

The maximum tension in the steel wire that can support elevator is given by

$T = \dfrac{1}{4} \times \text{stress} \times \text{area of cross-section}$

$= \dfrac{1}{4} \times 2. 2 \times {10}^{8} \times 4 \times {10}^{- 4}$

$= 2. 2 \times {10}^{4}Nm^{- 2}$

If $f$ be the maximum upward acceleration of the elevator, then

$T = m \left(g + f\right)$

$2. 2 \times {10}^{4} =1000 \left(10 + f\right)$

$⇒ f = 12ms^{- 2}$