The document Examples - Centre of Gravity and Centroid Mechanical Engineering Notes | EduRev is a part of the Mechanical Engineering Course Engineering Mechanics - Notes, Videos, MCQs & PPTs.

All you need of Mechanical Engineering at this link: Mechanical Engineering

Three particles (point masses) of mass 2 kg, 3 kg, and 3 kg, are welded to a straight massless rod as shown in the figure. Find the location of the center of mass of the assembly.

Solution Let us select the first mass, m1 D 2 kg, to be at the origin of our coordinate system with the x-axis along the rod. Since all the three masses lie on the x-axis, the center of mass will also lie on this axis. Let the center of mass be located at xcm on the x-axis. Then,

**Alternatively, **we could find the center of mass by first replacing the two 3 kg masses with a single 6 kg mass located in the middle of the two masses (the center of mass of the two equal masses) and then calculate the value of xcm for a two particle system consisting of the 2 kg mass and the 6 kg mass

Two particles of mass m1 = 1 kg and m2 = 2 kg are located at coordinates (1m, 2m) and (-2m, 5m), respectively, in the xy-plane. Find the location of their center of mass.

**Solution** Let be the position vector of the center of mass. Then,

Thus the center of mass is located at the coordinates(-1m, 4m).

A structure is made up of three point masses, m1 = 1 kg; m2 = 2 kg and m3 = 3 kg, connected rigidly by massless rods. At the moment of interest, the coordinates of the three masses are (1.25 m, 3 m), (2 m, 2 m), and (0.75 m, 0.5 m), respectively. Find the coordinates of the center of mass of the structure.

**Solution **Let (x_{cm} , y_{cm}) be the coordinates of the mass-center. Then from the definition of mass-center,

Similarly,

Thus the center of mass is located at the coordinates (1.25 m, 1.42 m).

Center of mass of a bent bar: A uniform bar of mass 4 kg is bent in the shape of an asymmetric â€™Zâ€™ as shown in the figure. Locate the center of mass of the bar.

**Solution.** Since the bar is uniform along its length, we can divide it into three straight segments. The mass of each segment is proportional to its length. Therefore, if we let m_{2} = m_{3} = m, then m_{1} = 2m; and m_{1} + m_{2} + m_{3} = 4m = 4 kg which gives m = 1 kg.

So

Find Centroid of the cross-section or Area in figs

Offer running on EduRev: __Apply code STAYHOME200__ to get INR 200 off on our premium plan EduRev Infinity!

30 videos|72 docs|65 tests

### Test: Centre Of Gravity

- Test | 15 ques | 30 min
### Test: Composite Bodies

- Test | 14 ques | 30 min
### Theorems of Pappus and Goldinus

- Doc | 1 pages
### Theorem 1 : Theorems of Pappus and Guldinus

- Video | 03:04 min
### Theorem 2 : Theorems of Pappus and Guldinus

- Video | 02:50 min
### Test: Theorem Of Pappus And Guldinus

- Test | 15 ques | 30 min

- Centre of Gravity for Composite Bodies
- Doc | 1 pages
- Centre of Mass for Composite Bodies
- Doc | 1 pages