JEE Advanced Physics Oscillations Miscellaneous Mixed Concept Problems

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Topic Question Set

Q 1 :

A person sitting inside an elevator performs a weighing experiment with an object of mass 50 kg. Suppose that the variation of the height $y$ (in m) of the elevator, from the ground, with time $t$ (in s) is given by $y = 8 [1 + \sin (\frac{2 π t}{T})] .$ where $T = 40 π s .$ Taking acceleration due to gravity, $g = 10 {m/s}^{2},$ the maximum variation of the object's weight (in N) as observed in the experiment is ______ [2025]

(2)

$Given y = 8 [1 + \sin (\frac{2 π t}{T})]$

$ω = \frac{2 π}{T} = \frac{2 π}{40 π} = \frac{1}{20}$

With respect to elevator, variation in weight will be

$Δ W = m {(Δ a)}_{\max}$

$Δ W = m \times 2 ω^{2} A$ $[∵ a_{\max} = A ω^{2}]$

Here elevator is performing SHM

$Δ W = 2 m {(\frac{2 π}{T})}^{2} \times A$

or, $Δ W = 2 \times 50 {(\frac{2 π}{40 π})}^{2} \times 8$

$Δ W = 2 \times 50 \times \frac{1}{400} \times 8$

$∴$ $Δ W = \frac{800}{400} = 2 N$

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