10. A simple pendulum set into vibration
completes an oscillation in time T. If
the length of the pendulum is
increased to 9 times its original
length, the new period of oscillation in
terms of T will be
А. 18.0 T
B. 9.0 T.
C. 4.5 T.
D 3.0 T
E. 0.1 T.

The new period of oscillation is D) 3.0 T

Explanation:

Simple Pendulum

A simple pendulum is a mechanical arrangement that describes periodic motion. The simple pendulum is made of a small bob of mass 'm' suspended by a thin inextensible string.

The period of a simple pendulum is given by

Where L is its length and g is the local acceleration of gravity.

If the length of the pendulum was increased to 9 times (L'=9L), the new period of oscillation will be:

Taking out the square root of 9 (3):

Substituting the original T:

The new period of oscillation is D) 3.0 T

force is mass*acceleration.

we have a very small mass: 11.4*0.001 kg

if we want 0.035n of force, we need an acceleration:

0.035 = 11.4*0.001*a

a = 0.035/(11.4*0.001) m/s^2