centre of mass of hollow hemisphere with an disc attached below of same radius R.
Answers
Total mass of that semicircular disc is given to be "m" and radius "r" so To detect position of centre of mass of semicircular disc we will use following formula y coordinate of centre of mass=∫mass of that small semicircular ring multiplied by Y coordinate of it's centre of mass/∫dm(mass of that small semicircular ring ) Now mass of the small ring would be equal mass per unit area multiplied by area of ring i.e 2m/π r^2 multiplied by circumference by thickness i.e πp dp.Y coordinate of the ring can be treated as Y coordinate of it's centre of mass .In one of our derivations Y coordinate of semicircular ring came out to be 2 multiplied by it's radius/π So y coordinate of centre of mass=∫2m/π r^2 multiplied by πp dp ×2pπ/ ∫dm an integration has upper and lower limit of r and zero respectively because we want to take all possible small rings of "0" to "r" radius. =