Question

Two pendulums of equal length but masses m and 2m. Find the ratio of their time period​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{T_{1}:T_{2}=1:1}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline\bold{Given :}} \\ \tt: \implies Mass \: of \: pendulums= m \: and \: 2m \\ \\ \tt: \implies Length \: of \: pendulums = l \\ \\ \red{\underline\bold{To \: Find:}} \\ \tt: \implies Ratio \: of \: time \: period =?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies \frac{ T_{1} }{ T_{2}} = \frac{2\pi \sqrt{ \frac{l}{g} } }{2\pi \sqrt{ \frac{l}{g} } } \\ \\ \tt: \implies \frac{ T_{1} }{ T_{2}} = \frac{2\pi}{2\pi} \sqrt{ \frac{l \times g}{l \times g} } \\ \\ \tt\circ \:Time Period\:is\:independent\:of\:mass \\ \\ \tt: \implies \frac{ T_{1} }{ T_{2}} = 1 \\ \\ \green{\tt: \implies T_{1} : T_{2} =1: 1}$