A lift of mass 1600 kg is supported by thick iron wire. If the maximum stress which the wire can withstand is and its radius is 4 mm

Question

A lift of mass 1600 kg is supported by thick iron wire. If the maximum stress which the wire can withstand is $4 \times 10^{8} N / m^{2}$ and its radius is 4 mm, then maximum acceleration the lift can take is _______ $m / s^{2}$ . $({take g=10 m/s}^{2} and π = 3.14)$ [2026]

Smart Achievers · Accepted Answer

(1)

$T - m g = m a$

$(σ π r^{2}) - m g = m a$

$\Rightarrow 4 \times 10^{8} π {(4 \times 10^{- 3})}^{2} - 16000 = 1600 a$

$\Rightarrow a = 2.56 {m/s}^{2}$

Solution

Q.
A lift of mass 1600 kg is supported by thick iron wire. If the maximum stress which the wire can withstand is $4 \times 10^{8} N / m^{2}$ and its radius is 4 mm, then maximum acceleration the lift can take is _______ $m / s^{2}$ . $({take g=10 m/s}^{2} and π = 3.14)$ [2026]

1 2.56

2 3.89

3 4.32

4 5.16

Ans.
(1)

$T - m g = m a$

$(σ π r^{2}) - m g = m a$

$\Rightarrow 4 \times 10^{8} π {(4 \times 10^{- 3})}^{2} - 16000 = 1600 a$

$\Rightarrow a = 2.56 {m/s}^{2}$

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