In the given figure, two elastic rods $A$ & $B$ are rigidly joined to end supports. $A$ small mass $‘m’$ is moving with velocity $v$ between the rods. All collisions are assumed to be elastic & the surface is given to be frictionless. The time period of small mass $‘m’$ will be : [$A=$ area of cross section, $Y =$ Young’s modulus, $L=$ length of each rod ; here, an elastic rod may be treated as a spring of spring constant $\frac{{YA}}{L}$ ]
In the given figure, two elastic rods $A$ & $B$ are rigidly joined to end supports. $A$ small mass $‘m’$ is moving with velocity $v$ between the rods. All collisions are assumed to be elastic & the surface is given to be frictionless. The time period of small mass $‘m’$ will be : [$A=$ area of cross section, $Y =$ Young’s modulus, $L=$ length of each rod ; here, an elastic rod may be treated as a spring of spring constant $\frac{{YA}}{L}$ ]
- A
$\frac{{2L}}{v} + 2\pi \sqrt {\frac{{mL}}{{AY}}}$
- B
$\frac{{2L}}{v} + 2\pi \sqrt {\frac{{2mL}}{{AY}}}$
- C
$\frac{{2L}}{v} + \pi \sqrt {\frac{{mL}}{{AY}}}$
- D
$\frac{{2L}}{v}$
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- [JEE MAIN 2023]
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