How to Find the Center of Gravity of a Cone and Hemisphere

TL;DR

To find the center of gravity (CG) of a composite solid made of a cone and a hemisphere, calculate the x-coordinate as half the cone's base diameter (20 cm) due to symmetry. The y-coordinate is found by using the volumes and distances of the solids, resulting in a CG at approximately 35.71 cm above the x-axis.

Transcript

hello friends here in this video i will be taking a problem on composite solid which is made up of hemisphere and cone so let us read the question what is given a solid cone of base diameter 40 centimeter and height 100 centimeter is welded to a hemisphere of same diameter find cg of solid composite figure now this is the question which is in front... Read More

Key Insights

• ❣️ The composite solid is symmetric about the y-axis, simplifying the calculation of the x-coordinate of the center of gravity.
• 🔇 The volume of a hemisphere is given by 2/3 * π * r^3, while the volume of a cone is 1/3 * π * r^2 * h.
• ❣️ Calculating the y-coordinate of the center of gravity involves considering the distance from the x-axis to the center of gravity of each solid separately.
• 🥡 The overall center of gravity is determined by taking into account the volumes and distances of each solid in relation to the x-axis.
• ❣️ The center of gravity is represented by its x and y coordinates, which intersect at a specific point on the composite solid.

Questions & Answers

Q: What is the problem discussed in the video?

The problem focuses on finding the center of gravity of a composite solid consisting of a cone and a hemisphere.

Q: How is the x-coordinate of the center of gravity determined?

The x-coordinate is half the diameter of the base of the cone, as the composite solid is symmetric about the y-axis.

Q: How is the y-coordinate of the center of gravity calculated?

The y-coordinate is calculated by considering the distances and volumes of the hemisphere and cone. The y-coordinate of the hemisphere's center of gravity is determined by subtracting 3r/8 from the radius, and the y-coordinate of the cone's center of gravity is found by adding the height divided by 4 to the radius.

Q: How is the overall center of gravity of the composite solid calculated?

The overall center of gravity (y-bar) is calculated using the formula: (v1 * y1 + v2 * y2) / (v1 + v2), where v1 and v2 are the volumes of the hemisphere and cone, and y1 and y2 are their respective y-coordinates.

Summary & Key Takeaways

• The problem involves a solid cone welded to a hemisphere, with given dimensions.

• To find the center of gravity, the dimensions and volumes of both solids are calculated.

• The x-coordinate of the center of gravity is found to be half the diameter of the cone's base, while the y-coordinate is determined using the volumes and distances of each solid.