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PhysicsSHMMiscellaneousEasy2 minPYQ_2020

PhysicsEasysingle choice

A pendulum has maximum kinetic energy $K_{1}$ . If its length is doubled keeping amplitude same then maximum kinetic energy becomes $K_{2}$ . Then relation between $K_{1}$ and $K_{2}$ is:

Options:

Answer:

Solution:

Maximum kinetic energy $= \frac{1}{2} m ω^{2} A^{2}$

$ω = \sqrt{\frac{g}{L}}$

$A = L θ$

$K E = \frac{1}{2} m \frac{g}{L} \times L^{2} θ^{2}$

$K E = \frac{1}{2} m g L θ^{2}$

If length is doubled

$K_{2} = \frac{1}{2} m g (2 L) θ^{2}$ [Here we are assuming angular amplitude is same]

$\frac{K_{1}}{K_{2}} = \frac{\frac{1}{2} m g l θ^{2}}{\frac{1}{2} m g (2 L) θ^{2}} = \frac{1}{2}$

$K_{2} = 2 K_{1}$

Stream:NTA_ABHYAS_NEETSubject:PhysicsTopic:SHMSubtopic:Miscellaneous

⏱ 2mℹ️ Source: PYQ_2020

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