If time period of two pendulums are in the ratio 3 : 5 find the ratio of their lengths
Answers
Answer:
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Explanation:
The pendulum period formula, T, is fairly simple: T = (L / g)1/2, where g is the acceleration due to gravity and L is the length of the string attached to the bob (or the mass). The dimensions of this quantity is a unit of time, such as seconds, hours or days.
Answer:
The ratio of their length is 4 : 1
Given:
The time period of two simple pendulum are in the ratio of 2 : 1
Solution:
Time period of a simple pendulum is calculated by the formula,
T=\frac{2 \pi \sqrt{l}}{g}T=
g
2π
l
Let us assume that the time period for first pendulum be T1 and for second pendulum be T2,
Thereby we have,
T_{1}=\frac{2 \pi \sqrt{l_{1}}}{g} \rightarrow (1)T
1
=
g
2π
l
1
→(1)
T_{2}=\frac{2 \pi \sqrt{l_{2}}}{g} \rightarrow (2)T
2
=
g
2π
l
2
→(2)
Dividing equation (1) and (2), we get,
\frac{T_{1}}{T_{2}}=\frac{\sqrt{l_{1}}}{\sqrt{l_{2}}}
T
2
T
1
=
l
2
l
1
On squaring both sides, we get,
\frac{T_{1}^{2}}{T_{2}^{2}}=\frac{l_{1}}{l_{2}}
T
2
2
T
1
2
=
l
2
l
1
\frac{l_{1}}{l_{2}}=\frac{2^{2}}{1^{2}}
l
2
l
1
=
1
2
2
2
\frac{l_{1}}{l_{2}}=\frac{4}{1}
l
2
l
1
=
1
4
Therefore, the length of the two simple pendulum be 4 : 1