Answer:
P = 0.27R from the center
Explanation:
Given,
The radius of the uniform circular plate, R = 2R
The radius of the hole, r = R
The center of the smaller circle from the center is, d = 0.8R
The center of mass of a circular disc with a hole in it given by the formula
P = dr²/R² - r²
Where P is the distance from the center of mass located in the line joining the two centers opposite to the hole.
Substituting the given values in the above equation,
P = 0.8R x R² / 4R² - R²
= 0.27R³/R²
= 0.27R
Hence the center of mass of plate is at a distant P = 0.27R from the center
Answer:
Some work input is lost to friction
Explanation:
The efficiency of a machine is defined as:
(1)
where
is the work output
is the work input
Due to the law of conservation of energy, the work output can never be larger than the work input (because energy cannot be created). Moreover, in real machines part of the work input is lost due to the presence of frictions: as a result, part of the energy in input is converted into thermal energy or other forms of energy, and so the work output is smaller than the work input, and so the ratio (1) becomes less than 1, and so the efficiency is less than 100%.