The length L of a simple pendulum varies directly as the square of its period T. If a pendulum with period 4 sec. is 64 cm long, find the length of pendulum whose period is 9 sec
A
96 cm
B
324 cm
C
36 cm
D
144 cm
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
\(L \propto T^2\)
\(L = kT^2\)
\(k = \frac{L}{T^2}\)
when T = 4, L = 64.
\(k = \frac{64}{4^2} = 4\)
\(L = 4T^2\)
when T = 9,
\(L = 4 \times 9^2 = 324cm\)
Source: Myschool Past Questions Archive (Record #8207)