JEE Main · 2024 · 31 Jan 2024 · Shift 2 · Elasticity & SHM

Two blocks of mass 2 kg and 4 kg are connected by a metal wire going over a smooth pulley as shown in figure. The radius of wire is

4.0 \times 1 0^{- 5}

m and Young's modulus of the metal is

2.0 \times 1 0^{11} N / m^{2}

. The longitudinal strain developed in the wire is

\frac{1}{α π}

. The value of

α

is ______. [Use

g = 10 m / s^{2}

]

Answer: 12

Solution

For the Atwood arrangement, the tension in the connecting wire is

T = \frac{2 m _{1} m _{2}}{m _{1} + m _{2}} g = \frac{2 \times 2 \times 4}{6} \times 10 = \frac{80}{3} N

The cross-sectional area of the wire is

A = π r^{2} = π (4 \times 1 0^{- 5})^{2} = 16 π \times 1 0^{- 10} m^{2}

The longitudinal strain is

strain = \frac{T}{A Y} = \frac{80/3}{16 π \times 1 0 ^{- 10} \times 2 \times 1 0 ^{11}} = \frac{80/3}{320 π} = \frac{1}{12 π}

Comparing with

\frac{1}{α π}

α = 12

JEE Main · 2024 · 31 Jan 2024 · Shift 2 · Integer answer