If the spring is suddenly cut while the rod is in motion, then: | TestHub

PhysicsMediummultiple choice

Passage / Comprehension

A conducting slider PQ of mass $m$ and length $ℓ$ is free to translate on two vertical smooth rails in the presence of gravity. The slider is connected with an initially relaxed, non-conducting spring of spring constant $k$ in a uniform magnetic field $B$ into the plane. The slider is released from rest and a capacitor is connected in the circuit.

If the spring is suddenly cut while the rod is in motion, then:

Options:(select one or more)

Answer:

C

Solution:

With the spring cut, the same current relation holds:
$I = CB ℓ a$
$(m + B^{2} ℓ^{2} C) a = m g$
$a = \frac{m g}{m + B ^{2} ℓ ^{2} C} = constant$ , independent of the direction of motion
Option (C) is correct.
(A) fails: without the spring there is no restoring force, hence no oscillation.
(B) fails: the magnetic drag here is proportional to acceleration (capacitor load), not velocity, so no terminal velocity exists.
(D) fails in general:
$Q = CB ℓ v$
$Q$ increases only while the rod speeds up downward; if the rod is moving upward when the spring is cut, $∣ v ∣$ and hence $Q$ first decrease.

Subject:PhysicsTopic:EMI/ACSubtopic:Motional & Rotational EMF

⏱ 3mℹ️ Source: QB

Physics - EMI/AC Question with Solution | TestHub

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