A lift of mass 1600 kg is supported by thick iron wire. If the maximum stress which the wire can withstand is $4 \times 10^{8} \mathrm{~N} / \mathrm{m}^{2}$ and its radius is 4 mm, then maximum acceleration the lift can take is ______ $\mathrm{m} / \mathrm{s}^{2}$. (take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$ and $\pi=3.14$)

JEE Main · 2026 · 06 Apr 2026 · Shift 1 · Elasticity & SHM

A lift of mass 1600 kg is supported by thick iron wire. If the maximum stress which the wire can withstand is

4 \times 1 0^{8} N / m^{2}

and its radius is 4 mm, then maximum acceleration the lift can take is ______

m / s^{2}

. (take

g = 10 m / s^{2}

and

π = 3.14

)

Answer: (A)

The wire sustains a maximum tension

T = σ π r^{2} = 4 \times 1 0^{8} \times 3.14 \times (4 \times 1 0^{- 3})^{2} = 20096

N. For the upward-accelerating lift,

T - m g = ma

, so

a = \frac{T - m g}{m} = \frac{20096 - 1600 \times 10}{1600} = \frac{4096}{1600}

. The maximum acceleration is

2.56 m/ s^{2}

JEE Main · 2026 · 06 Apr 2026 · Shift 1 · Single correct option