A simple pendulum of length L is constructed | vedclass

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

Question

(D) The pendulum swings with two different effective lengths during its motion.When the pendulum is on the left side,the effective length is $L_1 = L$

Vedclass · Accepted Answer

$\pi \sqrt{\frac{L}{g}} \left(1 + \frac{1}{\sqrt{3}}\right)$

Vedclass · Answer

(D) The pendulum swings with two different effective lengths during its motion.When the pendulum is on the left side,the effective length is $L_1 = L$. The time taken for a quarter oscillation is $t_1 = \frac{1}{4} T_1 = \frac{1}{4} (2\pi \sqrt{\frac{L}{g}}) = \frac{\pi}{2} \sqrt{\frac{L}{g}}$.When the pendulum is on the right side,it hits the peg at a distance $2L/3$ from the pivot. The effective length becomes $L_2 = L - 2L/3 = L/3$. The time taken for a quarter oscillation is $t_2 = \frac{1}{4} T_2 = \frac{1}{4} (2\pi \sqrt{\frac{L/3}{g}}) = \frac{\pi}{2} \sqrt{\frac{L}{3g}}$.The total time to return to the starting position is $T' = t_1 + t_2 + t_2 + t_1 = 2(t_1 + t_2)$.$T' = 2 \left( \frac{\pi}{2} \sqrt{\frac{L}{g}} + \frac{\pi}{2} \sqrt{\frac{L}{3g}} \right) = \pi \sqrt{\frac{L}{g}} \left( 1 + \frac{1}{\sqrt{3}} \right)$.

Similar Questions

$A$ hydrometer executes simple harmonic motion when it is pushed down vertically in a liquid of density $\rho$. If the mass of the hydrometer is $m$ and the radius of the hydrometer tube is $r$,then the time period of oscillation is

Two pendulums differ in lengths by $22 \ cm$. They oscillate at the same place such that one of them makes $15 \ oscillations$ and the other makes $18 \ oscillations$ during the same time. The lengths (in $cm$) of the pendulums are

The length of a simple pendulum is increased by $44\%$. The percentage increase in its time period will be ..... $\%$

At a place,the length of the oscillating simple pendulum is made $\frac{1}{4}$ times keeping the amplitude the same. Then,the total energy will be:

$A$ simple pendulum of length $l$ has a brass bob attached at its lower end. Its period is $T$. $A$ steel bob of the same size,having density $x$ times that of brass,replaces the brass bob. Its length is then changed such that the period becomes $2T$. What is the new length?

Vedclass Test Series

Exam Paper Generator

Online Exam Module