Question

Two simple pendulum, used at the same place have time period in the ratio of 1:15. If length of first pendulum is 0.75m, find the length of second's pendulum.​

Answer 1

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

$\green{\tt{\therefore{Length\:of\:second\:pendulum=168.75\:m}}}$

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

$\green{\underline \bold{Given :}} \\ \tt: \implies Ratio \: of \: time \: period = 1 : 15 \\ \\ \tt: \implies Length \: of \: first \: pendulum = 0.75 \: m \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Length \: of \: second \: pendulum = ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies \frac{ T_{1} }{T_{2}} = \huge{\frac{ \sqrt{ \frac{ l_{1} }{g} } }{ \sqrt{ \frac{ l_{2} }{g} } } } \\ \\ \tt \circ \: Where \: g \: is \: acceleration \: due \: to \: gravity \\ \\ \tt: \implies \frac{1}{15} = \huge{\bigg( \frac{ \frac{ l_{1}}{g}}{ \frac{ l_{2} }{g} } \bigg)^{ \frac{1}{2} }} \\ \\ \tt: \implies (\frac{1}{15})^{2} = \frac{ l_{1}}{g} \times \frac{g}{ l_{2}} \\ \\ \tt: \implies \frac{1}{225} = \frac{0.75}{ l_{2}} \\ \\ \tt: \implies l_{2} = 0.75 \times 225 \\ \\ \green{\tt: \implies l_{2} =168.75 \: m}$