Physics - Rotation Question with Solution | TestHub
For Q13-Q15, match each object of radius R with its centre-of-mass height from the ground and radius of gyration about the vertical axis through C.
Column 1: (I) solid hemisphere; (II) hemispherical shell; (III) half ring; (IV) half disc.
Column 2: (i) 5R/8; (ii) R/2; (iii) R - 4R/(3π); (iv) R - 2R/π.
Column 3: (P) R√(2/5); (Q) R√(2/3); (R) R/√2; (S) R/2.
Which of the following body has farthest centre of mass from C , what is its distance of centre of mass from ground and its radius of gyration about vertical axis passing through 'C' :-
Options:
Answer:
Solution:
The centre-of-mass heights are: solid hemisphere $5R/8$, shell $R/2$, half ring $R-2R/\pi$, and half disc $R-4R/(3\pi)$.
The half ring is farthest from the ground and its vertical-axis radius of gyration is $R/\sqrt2$. Thus (III, iv, R).
