Question

. If a pendulum-driven clock gains 5.00 s/day, what fractional change in pendulum length must be made for it to keep perfect time

Answer 1

Answer:

The appropriate response will be "Length must be increased by 0.012%".

Explanation:

The given values is:

ΔT = 5 s/day

Now,

⇒ $\frac{\Delta T}{T} =\frac{5}{24\times 60\times 60}$

On multiplying both sides by  "100", we get

⇒ $\frac{\Delta T}{T}\times 100 =\frac{500}{24\times 60\times 60}$

⇒ $\frac{\Delta T}{T}\times 100=0.005787$ (%)

∵  $T=2\pi\sqrt{\frac{l}{g} }$

On substituting the values, we get

⇒ $\frac{\Delta T}{T}$% = $\frac{1}{2}\times \frac{\Delta l}{l}$%

On applying cross multiplication, we get

⇒ $\frac{\Delta l}{l}$% = $2\times \frac{\Delta T}{T}$%

⇒        = $2\times 0.05787$

⇒        = $0.011574$

⇒        = $0.012$%