Vertical displacement of a plank with a body of mass 'm' on it is varying according to law y = sin ωt + √3 cos ωt. The minimum value of ω for which the mass just breaks off the plank and the time (t) it occurs first after t = 0 are given by: (y is positive vertically upwards)
1
\(\sqrt{\frac{\mathrm{g}}{2}}, \frac{\sqrt{2}}{6} \frac{\pi}{\sqrt{\mathrm{g}}}\)
2
\(\frac{\mathrm{g}}{\sqrt{2}}, \frac{2}{3} \sqrt{\frac{\pi}{\mathrm{g}}}\)
3
\(\sqrt{\frac{\mathrm{g}}{2}}, \frac{\pi}{3} \sqrt{\frac{2}{\mathrm{~g}}}\)
4
\(\sqrt{2 \mathrm{~g}}, \sqrt{\frac{2 \pi}{3 \mathrm{~g}}}\)