Question

For a pendulum with period of oscillation, T, if the mass of the bob is reduced by half what will be the new period of oscillation?
a. 2T
b. T/2
c. T
d. √2T
The pendulum is now swinging on Pluto. Calculate the new period of oscillation in terms of T, knowing that the gravity on Pluto is 1/16 that of Earth.

Answer 1

Answer:

c. T

and the new period is $T'=4T$

Explanation:

the period of a pendulum is given by:

$T=2\pi \sqrt{\frac{l}{g} }$

as we can see the period of oscillation of the pendulum does not depend on the mass, so if the mass is reduced this will not affect the period, it will remain the same.

The new period if thr pedulum oscilates on Pluto, will be calculated with the previous equation, but the gravity will be

$g'=\frac{1}{16}g$

where g is the gravity on earth: $g=9.8m/s^2$

so the new period:

$T=2\pi\sqrt{\frac{l}{g'} } =2\pi\sqrt{\frac{l}{\frac{1}{16} g} } =2\pi\sqrt{\frac{16l}{ g} } =2\pi \sqrt{16}\sqrt{\frac{l}{ g} } =4(2\pi \sqrt{\frac{l}{ g} })$

and we know that

$(2\pi \sqrt{\frac{l}{ g} })$ is the original period $T$

so the new period in terms of the orginal period is:

$T'=4T$