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

JEE Main · 2024 · 30 Jan 2024 · Shift 1 · Elasticity & SHM

Each of three blocks

P, Q

and R shown in figure has a mass of 3 kg . Each of the wire

A

and

B

has cross-sectional area

0.005 cm^{2}

and Young's modulus

2 \times 1 0^{11} N m^{- 2}

. Neglecting friction, the longitudinal strain on wire

B

is ____

\times 1 0^{- 4}

. (Take

g = 10 m / s^{2}

)

Answer: 2

With the pulley-block system, the common acceleration is

a = \frac{10}{3} m/ s^{2}

.

For the hanging block:

30 - T_{1} = 3 a \Rightarrow T_{1} = 20 N

(tension in wire B).

Stress

= \frac{T _{1}}{A} = \frac{20}{0.005 \times 1 0 ^{- 4}} = 4 \times 1 0^{7} N/ m^{2}

.

Strain

= \frac{stress}{Y} = \frac{4 \times 1 0 ^{7}}{2 \times 1 0 ^{11}} = 2 \times 1 0^{- 4}

JEE Main · 2024 · 30 Jan 2024 · Shift 1 · Integer answer