Question

Question 11 1 pts A simple pendulum completes one oscillation in 1.0 second. If the length and the mass of the pendulum are both doubled, how long will it take the pendulum to make one oscillation? 0.5 s 0.71 1 s 0 1.4s 0 2s

Answer 1

Time period of a pendulum is given by

$T = 2\pi \sqrt{\frac{L}{g}}$, [where L = length of pendulum]

We can see the time period does not depend on the mass of the object.

Therefore, we can write $T \propto \sqrt{L}$ .

When the length of the pendulum is doubled, then the new time period is T2.

therefore,

$\frac{T_{2}}{T_{1}} = \frac{\sqrt{L_{2}}}{\sqrt{L_{1}}}$

$\Rightarrow T_{2}= \frac{\sqrt{L_{2}}}{\sqrt{L_{1}}}*T_{1}$

  $= \frac{\sqrt{2*L_{1}}}{\sqrt{L_{1}}}*1 =\sqrt{2} = 1.4 s$[answer]

therefore, the correct option is 4th option. [answer]