Would the frequency of the angular simple harmonic motion (shm) of the balance wheel increase or decrease if the dimensions of the balance wheel were changed as described?

Yes the frequency of the angular simple harmonic motion (SHM) of the balance wheel increases three times if the dimensions of the balance wheel reduced to one-third of original dimensions.

Explanation:

Considering the complete question attached in figure below.

Time period for balance wheel is:

m = mass of balance wheel

R = radius of balance wheel.

Angular frequency is related to Time period as:

As dimensions of new balance wheel are one-third of their original values

moving ball hits still ball. mover stops, hit ball moves. momentum transfer.

answer: 802.3 kilo joules of energy represents 191.75 kilo calorie of energy.

explanation:

energy released during combustion of one mole methane = 802.3 kilo joules

if 1 kilo joule = 0.239006   kilo calorie

then ,802.3 kilo joule will be = 802.30.239006 kilo calorie

802.3 kilo joule = 191.75 kilo calorie

hence, the energy in kilo calorie is 191.75 kilo calorie.