Centre of mass of laminas and composite figures Quiz

1. Find the distance from the diameter of the centre of mass of a uniform semicircular lamina of radius $9$ cm.

• A. $\frac{18}{\pi}$ cm
• B. $3$ cm
• C. $\frac{12}{\pi}$ cm
• D. $4.5$ cm

2. Two uniform rectangular laminas have areas $10$ and $5$, with centres of mass at $x=2$ and $x=8$. Find $\bar{x}$ of the pair joined together.

• A. $4$
• B. $5$
• C. $3$
• D. $6$

3. A uniform disc of radius $6$ cm has a circular hole of radius $2$ cm cut out, with its centre $3$ cm from the centre $O$ of the disc. Where is the centre of mass of the remainder?

• A. $0.375$ cm from $O$, towards the hole
• B. $0.375$ cm from $O$, away from the hole
• C. $0.333$ cm from $O$, away from the hole
• D. $1.5$ cm from $O$, away from the hole

4. A triangular lamina has vertices $(0,0)$, $(6,0)$ and $(0,9)$. Find its centre of mass.

• A. $(3,\,4.5)$
• B. $(2,\,4.5)$
• C. $(3,\,3)$
• D. $(2,\,3)$

5. Which statement is true for every uniform lamina that has an axis of symmetry?

• A. Its centre of mass is at the midpoint of the axis
• B. Its centre of mass lies on the axis
• C. Its centre of mass is at a vertex
• D. Its centre of mass is outside the lamina