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. $\frac{m{v}_0^2}{AY}$
• B. $\frac{2m{v}_0^2}{AY}$
• C. $\frac{6m{v}_0^2}{AY}$
• D. $\frac{3m{v}_0^2}{AY}$

Answer 1

Answer: (C)

$\frac{T}{2m}+\frac{T}{m}=\frac{{\left(3v_0\right)}^2}{l}$
$T=\frac{6m{v}_0^2}{l}$
$Y=\frac{\frac{6m{v}_0^2}{lA}}{(\Delta l/Y)}\Rightarrow \Delta l=\frac{6m{v}_0^2}{AY}$