Question

if a 1 m long pendulum has a time period of 2 s, what should be the length of a pendulum of time period 4 s​

Answer 1

Given - Time period and length

Find - New length

Solution - Time period and length are related to each other as -

T1/T2 = ✓l1/l2

Keep the values in formula to find the value of l2.

$\frac{2}{4} = \sqrt{ \frac{1}{l2} }$

Taking square on both sides

$\frac{4}{16} = \frac{1}{l2}$

Performing cross multiplication

$l2 = \frac{16}{4}$

Performing division

$l2 = 4$

Hence, the length of a pendulum for time period 4 second will be 4 metres.

Answer 2

Answer:

Time period and length are related to each other as -

T1/T2 = ✓l1/l2

Keep the values in formula to find the value of l2.

\frac{2}{4} = \sqrt{ \frac{1}{l2} }

4

2

=

l2

1

Taking square on both sides

\frac{4}{16} = \frac{1}{l2}

16

4

=

l2

1

Performing cross multiplication

l2 = \frac{16}{4}l2=

4

16

Performing division

l2 = 4l2=4