Pendulum In Accelerated Frame

Question

A simple pendulum is suspended from the ceiling of a lift, and the lift accelerates downward with an acceleration equal to half of g. How does its time period change compared with the lift at rest?

RankGuru · Accepted Answer

Inside an accelerating lift the pendulum responds to an effective gravity $g_{eff}$ that combines true gravity with the pseudo-force from the frame's acceleration. For a lift accelerating downward with acceleration $a$, the effective gravity is reduced to $g_{eff} = g - a$, since the pseudo-force points upward relative to the bob. With $a = g/2$, we get $g_{eff} = g - g/2 = g/2$. The period is $T = 2\pi\sqrt{L/g_{eff}}$, so reducing the effective gravity to half its value increases the period by $\sqrt{g/(g/2)} = \sqrt{2}$, since the period varies inversely with the square root of the effective gravity acting on the bob. The option claiming a decrease by $\sqrt{2}$ reverses the direction of the effect, which would correspond to upward acceleration that strengthens effective gravity. The option of no change ignores the pseudo-force entirely. The option of doubling would require $g_{eff} = g/4$, meaning downward acceleration of $3g/4$, not $g/2$. This applies the NCERT principle of effective gravity in non-inertial frames. As a plausibility check, weaker effective gravity always slows a pendulum, so the period must lengthen, and the $\sqrt{2}$ factor follows the inverse-square-root dependence on gravity.

Pendulum In Accelerated Frame

Select the correct option:

🔒 Solution Hidden from View

More oscillations and waves Practice Questions

Comparing uniform circular motion with simple harmonic motion, the projection of a particle moving s...

Sound propagating through the air inside a long tube compresses and rarefies the medium along the di...

A stretched guitar string carries a tension of 80 N and has a linear mass density of 0.005 kg per me...

According to the Laplace correction, the speed of sound in a gas depends on which combination of gas...

Two waves of the same frequency travelling in a medium arrive at a point exactly out of phase with e...

A string fixed at both ends and one metre long vibrates in its fundamental mode, so what is the wave...

An organ pipe closed at one end and open at the other resonates in its lowest mode, so which harmoni...

A piano tuner sounds a reference fork of 256 hertz alongside a slightly mistuned string and hears fo...

An ambulance siren emitting 400 hertz approaches a stationary listener at 30 metres per second while...

When an oscillating particle in simple harmonic motion is at half of its amplitude, what fraction of...

A block of mass 2 kg attached to a light spring of force constant 200 N per metre oscillates on a fr...

Two identical springs each of force constant k are connected in parallel and support a mass m, so ho...

About This Question

Solution