A Half Ring

Q. The centre of mass of a semi-circular ring lies $5\text{cm}$ above the centre of the semi-circle. What is the circumference of the ring?

1. $20.67\text{cm}$
2. $27.48\text{cm}$
3. $24.67\text{cm}$
4. $18.56\text{cm}$

Q. A circular wire frame is made of two uniform semicircular wires of same radius and of mass per unit lengths $\lambda$ and $2\lambda$ as shown in figure. Which of the following options is/are true?

1. $x_{cm}=0$
2. $x_{cm}<0$
3. $y_{cm}<0$
4. $y_{cm}=0$

Q. A circular wire frame is made of two uniform semicircular wires of same radius and of mass per unit lengths $\lambda$ and $2\lambda$ as shown in figure. Which of the following options is/are true?

1. $x_{cm}=0$
2. $x_{cm}<0$
3. $y_{cm}<0$
4. $y_{cm}=0$