Question

The C.G of a quarter circular area with radius 10 cm is

Answer 1

Answer:

Without going into the calculus of centroids and centers of gravity, the formula you can use for this quarter circle is x=0.900R. Create your wire bend with the radius of 10cm and the 90degree bend. Lay it out on paper. The origin of the radius and the 90degree bend is at x=0. Split the wire bend in half with another radius line. That’s your x-line. Since your R= 10cm, the formula gives you x=. 0.900• 10cm= 9cm out along the x-axis from the origin. So the CG is a point of balance in space around which the wire will rotate when thrown or the point about which it will balance

Answer 2

Final Answer:

The C.G of a quarter circular area with radius 10 cm is given by the coordinates (4.24cm, 4.24 cm) in the x-y plane.

Given:

A quarter circular area with the given radius 10 cm.

To Find:

The C.G of the quarter circular area having the radius 10 cm.

Explanation:

The full form of C.G is Centre of Gravity. The centers of gravity are, generally located at the centroids of the respective geometric figures. The CG is the point of balance for the given geometric shape in space about which the said shape will rotate keeping the absolute balance in motion.

The area of a quarter circle with a radius of r cm is $\frac{\pi r^2}{4}$ sq. cm.

The coordinates of the C.G. of the quarter circle is given by $(\frac{4r}{3 \pi} , \frac{4r}{3 \pi})$.

Step 1 of 2

It is assumed that the quarter circular area with radius 10 cm is lying on the first quadrant of the two-dimensional cartesian coordinate system.

Hence, the C.G of the quarter circular area with radius 10 cm can be found out by putting the value of r=10 in the above formula.

Step 2 of 2

The C.G of a quarter circular area with radius 10 cm is having the following coordinates in the first quadrant of the two-dimensional cartesian coordinate system.

$\frac{4r}{3 \pi} , \frac{4r}{3 \pi}\\=(\frac{4}{3 \pi} \times 10) , (\frac{4r}{3 \pi} \times 10)\\=\frac{40}{3 \pi} , \frac{40}{3 \pi}\\=4.24, 4.24$

The required centre of gravity of a quarter circular area with radius 10 cm is given by the coordinates (4.24cm, 4.24 cm) in the x-y plane.

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