A simple pendulum is taken to a place where i | vedclass

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

Question

(C) The time period of a simple pendulum is given by $T = 2\pi \sqrt{\frac{\ell}{g'}}$.At a height $h = R$ (where $R$ is the radius of the Earth), the

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(C) The time period of a simple pendulum is given by $T = 2\pi \sqrt{\frac{\ell}{g'}}$.At a height $h = R$ (where $R$ is the radius of the Earth), the acceleration due to gravity $g'$ is given by $g' = g \left( \frac{R}{R+h} ight)^2 = g \left( \frac{R}{R+R} ight)^2 = \frac{g}{4}$.Given $g = \pi^2 \ m/s^2$ at the surface, the effective gravity at height $h$ is $g' = \frac{\pi^2}{4} \ m/s^2$.Substituting the values $\ell = 4.0 \ m$ and $g' = \frac{\pi^2}{4} \ m/s^2$ into the time period formula:$T = 2\pi \sqrt{\frac{4}{\pi^2 / 4}} = 2\pi \sqrt{\frac{16}{\pi^2}} = 2\pi 	imes \frac{4}{\pi} = 8 \ s$.

$A$ simple pendulum is taken to a place where its distance from the Earth's surface is equal to the radius of the Earth. Calculate the time period of small oscillations if the length of the string is $4.0 \ m$. (Take $g = \pi^2 \ m/s^2$ at the surface of the Earth.) (in $s$)

Similar Questions

$A$ bob of a simple pendulum has mass $m$ and is oscillating with an amplitude $a$. If the length of the pendulum is $L$,then the maximum tension in the string is (given $\cos 0^{\circ}=1, g=$ acceleration due to gravity):

The period of a simple pendulum is measured as $T$ in a stationary lift. If the lift moves upwards with an acceleration of $5g$,the new period will be:

$A$ second's pendulum is mounted in a rocket. Its period of oscillation decreases when the rocket

$A$ pendulum of length $l = 1\,m$ is released from $\theta_0 = 60^\circ$. The rate of change of speed of the bob at $\theta = 30^\circ$ is ........ $m/s^2$ $(g = 10\,m/s^2)$.

If the length of a clock pendulum increases by $0.2 \%$ due to atmospheric temperature rise,then the loss in time of the clock per day is ........... $s$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module