Two pendulums have time periods T and frac{5T | vedclass

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

Question

(B) Let the time periods be $T_1 = T$ and $T_2 = \frac{5T}{4}$.Since $T_2 > T_1$,the pendulum with time period $T_2$ is the bigger pendulum.After the

Vedclass · Accepted Answer

$90$

Vedclass · Answer

(B) Let the time periods be $T_1 = T$ and $T_2 = \frac{5T}{4}$.Since $T_2 > T_1$,the pendulum with time period $T_2$ is the bigger pendulum.After the bigger pendulum completes one oscillation,the time elapsed is $t = T_2 = \frac{5T}{4}$.In this time $t$,the number of oscillations completed by the smaller pendulum is $n = \frac{t}{T_1} = \frac{5T/4}{T} = \frac{5}{4} = 1.25$ oscillations.This means the smaller pendulum completes $1$ full oscillation and an additional $0.25$ (or $\frac{1}{4}$) of an oscillation.At $t = T_2$,the bigger pendulum is at the mean position (phase $\phi_2 = 2\pi$ or $0$).The smaller pendulum has completed $1.25$ oscillations,meaning it is at the positive extreme position (phase $\phi_1 = 1.25 	imes 2\pi = 2.5\pi = 2\pi + \frac{\pi}{2}$).The phase difference is $\Delta\phi = |\phi_1 - \phi_2| = \frac{\pi}{2} = 90^o$.

Column-$I$	Column-$II$
$(a)$ $T^2 \to l$	$(i)$ Linear
$(b)$ $T^2 \to g$	$(ii)$ Parabolic
$(c)$ $T \to l$	$(iii)$ Hyperbolic

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 $^o$)?

Similar Questions

$A$ person measures a time period of a simple pendulum inside a stationary lift and finds it to be $T$. If the lift starts accelerating upwards with an acceleration $\left(\frac{g}{3}\right)$,the time period of the pendulum will be

The ratio of frequencies of oscillations of two simple pendulums is $3: 4$,then their lengths are in the ratio

The amplitude of a simple pendulum is $10 \ cm$. When the pendulum is at a displacement of $4 \ cm$ from the mean position,the ratio of kinetic and potential energies at that point is

In the following table, the relation of the graph in column-$I$ and the shape of the graph in column-$II$ is shown. Match them appropriately.
Column-$I$ Column-$II$
$(a)$ $T^2 \to l$ $(i)$ Linear
$(b)$ $T^2 \to g$ $(ii)$ Parabolic
$(c)$ $T \to l$ $(iii)$ Hyperbolic

Vedclass Test Series

Exam Paper Generator

Online Exam Module