A simple pendulum is suspended in a car. The | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The car moves with an acceleration $a$. Given the position equation $x = \frac{g}{2} \sqrt{3} t^2$,we differentiate twice with respect to time $t$

Vedclass · Accepted Answer

$2\pi \sqrt{\frac{l}{2g}}$

Vedclass · Answer

(C) The car moves with an acceleration $a$. Given the position equation $x = \frac{g}{2} \sqrt{3} t^2$,we differentiate twice with respect to time $t$ to find the acceleration:$v = \frac{dx}{dt} = g \sqrt{3} t$$a = \frac{dv}{dt} = g \sqrt{3}$In the frame of the car,the pendulum experiences a pseudo-force in the direction opposite to the acceleration. The effective acceleration due to gravity $g_{eff}$ is the vector sum of the gravitational acceleration $g$ (downwards) and the pseudo-acceleration $a$ (backwards):$g_{eff} = \sqrt{g^2 + a^2} = \sqrt{g^2 + (g \sqrt{3})^2} = \sqrt{g^2 + 3g^2} = \sqrt{4g^2} = 2g$The time period of a simple pendulum is given by $T = 2\pi \sqrt{\frac{l}{g_{eff}}}$.Substituting $g_{eff} = 2g$,we get $T = 2\pi \sqrt{\frac{l}{2g}}$.Thus,the correct option is $C$.

$A$ simple pendulum is suspended in a car. The car starts moving on a horizontal road according to the equation $x = \frac{g}{2} \sqrt{3} t^2$. Find the time period of oscillation of the pendulum.

Similar Questions

The time period of a simple pendulum,on a satellite orbiting the Earth,is

$A$ coin is placed on a horizontal plate. The plate performs $S.H.M.$ vertically with an angular frequency $\omega$. The amplitude $A$ of oscillations is gradually increased. The coin will lose contact with the plate for the first time when the amplitude is ($g =$ acceleration due to gravity).

$A$ simple pendulum of frequency $f$ has a metal bob. If the bob is charged negatively and is allowed to oscillate above a large positively charged plate,the frequency will be:

The breaking strength of the string of a simple pendulum is twice the weight of the bob. The bob is released from rest when the string is horizontal. At what angle $\theta$ with the vertical will the string break?

$A$ pendulum clock is set to give correct time at sea level. This clock is moved to a hill station at an altitude of $2500 \ m$ above sea level. In order to keep correct time at the hill station,the length of the pendulum:

Vedclass Test Series

Exam Paper Generator

Online Exam Module