Question

Two point masses of mass m and $2m$ placed on smooth horizontal plane are connected by a light rod of length $l$ . Masses are given velocities in horizontal plane perpendicular to rod as shown. If area of cross section of rod is A and Young's modulus is $Y$ , then elongation in the rod, will be

• A. $\frac{m v_{0}^{2}}{A Y}$
• B. $\frac{2 m v_{0}^{2}}{A Y}$
• C. $\frac{6 m v_{0}^{2}}{A Y}$
• D. $\frac{3 m v_{0}^{2}}{A Y}$

Answer 1

Answer: (C)

$\frac{T}{2 m}+\frac{T}{m}=\frac{\left(3 v_{0}\right)^{2}}{l}$
$T=\frac{6 m v_{0}^{2}}{l}$
$Y=\frac{\frac{6 m v_{0}^{2}}{l A}}{\left(\right. \Delta l / Y \left.\right)}\Rightarrow \Delta l=\frac{6 m v_{0}^{2}}{A Y}$