A bob of a simple pendulum has mass m and is | vedclass

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

Question

(A) The tension in the string is maximum when the bob passes through the mean position.At the mean position,the forces acting on the bob are the tensi

Vedclass · Accepted Answer

$mg\left[1+\left(\frac{a}{L}\right)^{2}\right]$

Vedclass · Answer

(A) The tension in the string is maximum when the bob passes through the mean position.At the mean position,the forces acting on the bob are the tension $T$ upwards and weight $mg$ downwards. The net centripetal force is provided by the difference between tension and weight:$T_{\max} - mg = \frac{mV^{2}}{L} \implies T_{\max} = mg + \frac{mV^{2}}{L} \dots (1)$In Simple Harmonic Motion $(SHM)$,the velocity at the mean position is given by $V = a\omega$.For a simple pendulum,the angular frequency is $\omega = \sqrt{\frac{g}{L}}$.Thus,$V = a\sqrt{\frac{g}{L}}$,which implies $V^{2} = a^{2}\frac{g}{L}$.Substituting this value of $V^{2}$ into $Eq. (1)$:$T_{\max} = mg + \frac{m}{L} \left(a^{2}\frac{g}{L}\right) = mg + \frac{mga^{2}}{L^{2}} = mg \left[1 + \left(\frac{a}{L}\right)^{2}\right]$.

$A$ 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):

Similar Questions

The period of a simple pendulum gets doubled when

Two pendulums have time periods $T$ and $\frac{5T}{4}$. They start $S.H.M.$ at the same time from the mean position. What will be the phase difference between them after the bigger pendulum has completed one oscillation (in $^o$)?

$A$ simple pendulum oscillating in air has period $T.$ The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is $\frac{1}{16}$ of the material of the bob. If the bob is inside the liquid all the time,its period of oscillation in this liquid is:

$A$ simple pendulum is executing simple harmonic motion with a time period $T$. If the length of the pendulum is increased by $21\%$,the percentage increase in the time period of the pendulum of increased length is ..... $\%$

Vedclass Test Series

Exam Paper Generator

Online Exam Module