The time period of a simple pendulum is T. Wh | 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 $T = 2 \pi \sqrt{\frac{l}{g}}$,so $T^2 = 4 \pi^2 \left(\frac{l}{g}\right) \quad ...(i)$When the l

Vedclass · Accepted Answer

$2 T^2=T_1^2+T_2^2$

Vedclass · Answer

(C) The time period of a simple pendulum is given by $T = 2 \pi \sqrt{\frac{l}{g}}$,so $T^2 = 4 \pi^2 \left(\frac{l}{g}\right) \quad ...(i)$When the length is increased by $10 \ cm$,the new time period $T_1$ is given by $T_1^2 = 4 \pi^2 \left(\frac{l+10}{g}\right) \quad ...(ii)$When the length is decreased by $10 \ cm$,the new time period $T_2$ is given by $T_2^2 = 4 \pi^2 \left(\frac{l-10}{g}\right) \quad ...(iii)$Adding equations $(ii)$ and $(iii)$,we get:$T_1^2 + T_2^2 = 4 \pi^2 \left(\frac{l+10}{g}\right) + 4 \pi^2 \left(\frac{l-10}{g}\right)$$T_1^2 + T_2^2 = \frac{4 \pi^2}{g} (l + 10 + l - 10)$$T_1^2 + T_2^2 = \frac{4 \pi^2}{g} (2l)$$T_1^2 + T_2^2 = 2 \left(4 \pi^2 \frac{l}{g}\right)$Substituting equation $(i)$ into this,we get:$T_1^2 + T_2^2 = 2 T^2$

The time period of a simple pendulum is $T$. When the length is increased by $10 \ cm$,its period is $T_1$. When the length is decreased by $10 \ cm$,its period is $T_2$. Then,the relation between $T, T_1$,and $T_2$ is

Similar Questions

What happens to the time period of a simple pendulum when it is taken to the moon's surface from the earth's surface?

$A$ pendulum clock keeps correct time at $0^{\circ}C$. If its mean coefficient of linear expansion is $\alpha /^{\circ}C$,what is the loss in seconds per day by the clock if the temperature rises by $t^{\circ}C$?

The time period of a simple pendulum,on a satellite orbiting the Earth,is

$A$ 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?

$A$ pendulum suspended from the ceiling of a train oscillates with a time period $2 \ s$,when the train is accelerating at $10 \ m/s^2$. What will be its time period when the train retards at $10 \ m/s^2$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module