Each of three blocks P, Q and R shown in figure has a mass of 3 kg. Each of the wires A and B has cross-sectional area 0.005 cm² and Young's modulus 2 × 10¹¹ N m⁻². Neglecting friction, the longitudinal strain on wire B is ________ × 10⁻⁴. (Take g = 10 m/s²) Numerical answer type. Work it out, then open the answer.

Answer: 2. PQT_BP + Q (6 kg)T_B = (6 kg) a = 6 x 10/3 = 20 Na = 30 N / 9 kg = 10/3 m/s² Whole system: a = (mR g)/(mP + mQ + mR) = 30/9 = 10/3 m/s² Wire B pulls both P and Q: TB = (mP + mQ)a = 6 × 10/3 = 20 N A = 0.005 cm² = 5 × 10⁻⁷ m² Strain = TB/AY = 205 × 10⁻⁷ × 2 × 10¹¹ = 2 × 10⁻⁴ Answer: 2

Each of three blocks P, Q and R shown in figure has a mass of 3 kg… | JEE Main 2024 (30 Jan, Shift 1)

Q8JEE Main 2024 · 30 JAN · SHIFT 1Medium

Elastic Behaviour, Stress & Strain

Each of three blocks $P, Q$ and $R$ shown in figure has a mass of $3\text{ kg}$ . Each of the wires $A$ and $B$ has cross-sectional area $0.005\text{ cm}^2$ and Young's modulus $2 \times 10^{11}\text{ N m}^{-2}$ . Neglecting friction, the longitudinal strain on wire $B$ is ________ $\times 10^{-4}$ . (Take $g = 10\text{ m/s}^2$ )

Numerical answer type. Work it out, then open the answer.

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Answer: 2

Whole system: $a = \frac{m_R g}{m_P + m_Q + m_R} = \frac{30}{9} = \frac{10}{3}\ \text{m/s}^2$
Wire $B$ pulls both $P$ and $Q$ : $T_B = (m_P + m_Q)a = 6 \times \frac{10}{3} = 20\ \text{N}$
$A = 0.005\ \text{cm}^2 = 5 \times 10^{-7}\ \text{m}^2$
Strain $= \frac{T_B}{AY} = \frac{20}{5 \times 10^{-7} \times 2 \times 10^{11}} = 2 \times 10^{-4}$
Answer: $2$

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