First slide

Applications of SHM

Question

A simple pendulum of length ' $L_{1}$ ' has a time period ' $T_{1}$ ' and another pendulum of length ' $L_{2}$ ' has time period ' $T_{2}$ '. Then the time period of pendulum of length $(L_{1} + L_{2})$ is

Moderate

A

$T_{1} + T_{2}$
B

$\sqrt{T_{1} + T_{2}}$
C

$\sqrt{T_{1} T_{2}}$
D

$\sqrt{{T_{1}}^{2} {+T}_{2}^{2}}$

Solution

$t i m e p e r i o d o f a s i m p l e p e n d u l u m i s T_{1} = 2π \sqrt{\frac{l_{1}}{g}} T_{2} = 2π \sqrt{\frac{l_{2}}{g}} {⇒T}_{1}^{2} α l_{1} ----(1) {⇒ T}_{2}^{2} α l_{2} ----(2) T = 2π \sqrt{\frac{l_{1} + l_{2}}{g}} \Rightarrow T^{2} α l_{1} + l_{2} ----(3) s u b s t i t u t e (1), (2) i n (3) T^{2} α {T_{1}}^{2} + {T_{2}}^{2} \Rightarrow T α \sqrt{{T_{1}}^{2} + {T_{2}}^{2}}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App