Circular Motion

Length of $\text{arc}, I=4.4 \text{ ly}=4.4 \times 9.46 \times 10^{15}$ $=4.1624 \times 10^{16} \text{ m}$ $[\because 1 \text{ Iy}=9.46 \times 10^{15} \text{ m}]$ Angle subtended by arc, θ = 4 s Number of revolution, n = 4 Speed of body, We know that, length of arc subtended by an angle, $I=R \theta$ Here, R = radius of arc. Substituting the values in above expression, we get $4.1624 \times 10^{16}=R \times 4 \times \left(\frac{1^{\circ}}{3600}\right) \times \left(\frac{\pi}{180^{\circ}}\right)$ $\left(\because 1 \text{ s}=\frac{1}{3600} \text{ degree}\right)$ $R=2.146 \times 10^{21} \text{ m}$ We know that, time = distance/speed $t=\frac{n \times 2 \pi R}{V}$ (∵ Distance = n × length of circular path ) Substituting the values in above expression, we get $t=\frac{4 \times 2 \pi \times 2.146 \times 10^{21}}{1.2 \times 10^{12}}$ $=4.5 \times 10^{10} \text{ s}$ Thus, the time required is $4.5 \times 10^{10} \text{ s}$.