Question 8.11: Find the centre of mass of a solid hemisphere of radius r.

An Introduction to Mathematics for Engineers: Mechanics

Find the centre of mass of a solid hemisphere of radius r.

The "Step-by-Step Explanation" refers to a detailed and sequential breakdown of the solution or reasoning behind the answer. This comprehensive explanation walks through each step of the answer, offering you clarity and understanding.
Our explanations are based on the best information we have, but they may not always be right or fit every situation.

The blue check mark means that this solution has been answered and checked by an expert. This guarantees that the final answer is accurate.
Learn more on how we answer questions.

This Question has been Answered.

Already have an account?

Related Answered Questions

Question: 8.13

i) Find the position of the centre of mass of a uniform hemispherical bowl of thickness 1 cm and inside radius 9 cm. ii) A light handle AB of length 18 cm is attached to a point A on the rim of the bowl in such a way that the line AB passes through the centre of the hemisphere. What angle does AB ...

Verified Answer:

i) Think of the bowl as a solid hemisphere of radi...

Question: 8.16

Find the co-ordinates of the centroid of the region between the curve y = 4 – x² and the positive x and y axes. ...

Verified Answer:

It is best to find the area, A, first. In this cas...

Question: 8.15

Find the position of the centre of mass of a uniform semi-circular lamina of radius r. ...

Verified Answer:

The diagram below shows the lamina. By symmetry, [...

Question: 8.14

A traffic cone is modelled as a hollow cone of height 45 cm standing on a heavy cylindrical base of radius 20 cm and height 5 cm. The mass of the base is twice that of the cone. i) Find the position of the centre of mass of the traffic cone. ii) What is the angle of the steepest slope it can be ...

Verified Answer:

i) You can put the information in a table. Co...

Question: 8.12

Find the position of the centre of mass of the solid of revolution formed when the region between the curve y = 2e^x, the lines x = 0 and x = 2, and the x axis is rotated through 360° about the x axis. ...

Verified Answer:

The diagrams show the region and the solid obtaine...

Question: 8.10

Find the volume of a spherical ball of radius 2 cm. ...

Verified Answer:

The sphere is formed by rotating the circle x² + y...

Question: 8.9

Find the volume of revolution formed when the region between the curve y = x² + 2 , the x axis and the lines x = 1 and x = 3 is rotated completely about the x axis. ...

Verified Answer:

The volume is: V =

...

Question: 8.8

A metal disc of radius 15 cm has a hole of radius 5 cm cut in it as shown in figure 8.15. Find the centre of mass of the disc. ...

Verified Answer:

Think of the original uncut disc as a composite bo...

Question: 8.7

Figure 8.14 shows a square table of side 2 m which is supported by four legs, each 1 m high, situated at the corners of a 1m square. The mass of each leg is 1 kg and that of the table top 2 kg. The legs and the top are uniform. A small heavy object of mass 6 kg is placed on one corner of the table. ...

Verified Answer:

i) Let the co-ordinates of the centre of mass be [...

Question: 8.6

Find the centre of mass of a body consisting of a square plate of mass 3 kg and side length 2 m, with small objects of mass 1 kg, 2 kg, 4 kg and 5 kg at the corners of the square. ...

Verified Answer:

Figure 8.13 shows the square plate, with the origi...