Question

Length of second's pendulum is $100cm$. Find the length of a pendulum whose time peroid is $1.4s$.(in $cm$)

• A. $1.0$
  
• B. $98.0$
• C. $39.0$
• D. $49.0$

Answer 1

The correct option is D $49.0$

$T_1=2s$; $l_1=100cm$; $T_2=1.4s$; $l_2=?$
$\frac{T_1}{T_2}=\sqrt{\frac{l_1}{l_2}}$
$\therefore \frac{2}{1.4}=\sqrt{\frac{100}{l}}$

Squaring both sides, we get:

$\frac{4}{1.96}=\frac{100}{l_2}\Rightarrow l_2=\frac{100\times 1.96}{4}=49.0cm$