/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 18 A person measures the time perio... [FREE SOLUTION] | 91影视

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Chapter 9: Problem 18

A person measures the time period of a simple pendulum inside a stationary lift and finds it to be \(T\). If the lift starts accelerating upwards with an acceleration of \(\mathrm{g} / 3\), the time period of the pendulum will be (A) \(\sqrt{3} T\) (B) \(\frac{\sqrt{3}}{2} T\) (C) \(T / \sqrt{3}\) (D) \(T / 3\)

Short Answer

Expert verified
The new time period of the pendulum when the lift accelerates upwards with an acceleration of \(g/3\) is (B) \(\frac{\sqrt{3}}{2} T\).

Step by step solution

01

Recall the formula for the time period of a simple pendulum

The time period T of a simple pendulum is given by the formula: \(T = 2\pi \sqrt{\frac{l}{g}}\), where l is the length of the pendulum and g is the acceleration due to gravity.
02

Modify the formula considering the acceleration of the lift

When the lift accelerates upward with acceleration \(a = \frac{g}{3}\), the effective acceleration experienced by the pendulum is \(g' = g + a\). Therefore, the modified equation for the time period under acceleration is given by \(T' = 2\pi \sqrt{\frac{l}{g'}}\).
03

Substitute values for g and a

Substituting the given values for acceleration due to gravity (g) and the lift's upward acceleration (a) into the modified equation: \(T' = 2\pi \sqrt{\frac{l}{g + \frac{g}{3}}}\).
04

Simplify the equation

Simplify the equation: \(T' = 2\pi \sqrt{\frac{l}{\frac{4g}{3}}}\).
05

Compare the new time period with the original time period

To find the relation between T' and T, we'll compare the two equations: \(\frac{T'}{T} = \frac{2\pi \sqrt{\frac{l}{\frac{4g}{3}}}}{2\pi \sqrt{\frac{l}{g}}}\). Simplifying the equation, we get: \(\frac{T'}{T} = \sqrt{\frac{3}{4}}\).
06

Find the value of T'

Now, we can find the value of T' by multiplying both sides of the equation by T: \(T'= TT'\). Therefore, \(T' = \frac{\sqrt{3}}{2}T\). The correct answer is (B) \(\frac{\sqrt{3}}{2} T\).

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