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

$A$ child is sitting on a swing which performs $S.H.M$. It has minimum and maximum heights from the ground of $0.75 \,m$ and $2 \,m$ respectively. Its maximum speed will be $\left[g=10 \,m/s^2\right]$

If the metal bob of a simple pendulum is replaced by a wooden bob, then its time period will

$A$ pendulum is oscillating at a frequency of $8 \,Hz$. Suddenly, the string of the pendulum is clamped at its midpoint. What is the new frequency of oscillations (in $\,Hz$)?

$A$ simple pendulum keeps correct time at $0^{\circ}C$. At $25^{\circ}C$,it loses $12.5 \, s$ in a day. What is the coefficient of linear expansion of the metal of the pendulum?

$A$ simple pendulum,suspended from the ceiling of a stationary van,has time period $T$. If the van starts moving with a uniform velocity,the period of the pendulum will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module