Physics - Elasticity Question with Solution | TestHub

PhysicsElasticityMiscellaneousMedium2 minQB

PhysicsMediumsingle choice

A rod of mass m , uniform cross sectional area A and length L is accelerated by applying force F as shown in figure on a smooth surface. If Young's modulus of elasticity of the material of rod is Y . (Consider x as measured from the right end)

Options:

Answer:

Solution:

$ma = F \Rightarrow a = \frac{F}{m}$

For portion $BC$ : $m_{BC} a = T \Rightarrow T = (\frac{mx}{L}) a$ ; $T = (\frac{mx}{L}) \frac{F}{m} = \frac{Fx}{L}$ .

$s t ress = \frac{Fx}{AL}$

$\frac{d ℓ}{dx} = \frac{stress}{Y} = \frac{Fx}{LAY} \Rightarrow Δ ℓ = \int_{0}^{ℓ} \frac{Fx}{LAY} dx \Rightarrow \frac{Δ ℓ}{L} = \frac{F}{2 AY}$

Stream:JEESubject:PhysicsTopic:ElasticitySubtopic:Miscellaneous

⏱ 2mℹ️ Source: QB

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