Question
Download Solution PDFThe centre of gravity of a (10 × 15 × 5) cm T section (From bottom) will be
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Centroid:
- The centroid of a shape represents the point at which the area of the section is evenly distributed.
- If the area is doubly symmetric about two orthogonal axes, the centroid lies at the intersection of those axes. If the area is symmetric about only one axis, then the centroid lies somewhere along that axis.
- It is also defined as a point where the whole body mass can be concentrated for evaluating the physical and numerical quantities.
Formula for centroid.
\({{\rm{x}}_{\rm{c}}} = \frac{{{{\rm{A}}_1}{{\rm{x}}_1} + {{\rm{A}}_2}{{\rm{x}}_2}}}{{{{\rm{A}}_1} + {{\rm{A}}_2}}}{\rm{\;and\;}}{{\rm{y}}_{\rm{c}}} = \frac{{{{\rm{A}}_1}{{\rm{y}}_1} + {{\rm{a}}_2}{{\rm{y}}_2}}}{{{{\rm{A}}_1} + {{\rm{A}}_2}}}\)
Calculation:
Centre of gravity:
\(\bar y = \frac{{{A_1}{y_1} + {A_2}{y_2}}}{{{A_1} + {A_2}}} = \frac{{\left( {10 \times 5} \right) \times 12.5 + \left( {10 \times 5} \right) \times 5}}{{\left( {10 \times 5} \right) + \left( {10 \times 5} \right)}} = 8.75\;cm\;\left( {from\;bottom} \right)\)
Additional Information
The centroid for the different sections are as follows:
Last updated on May 28, 2025
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