Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Classical Mechanics Euler’s Dynamical Equations For The Motion
Consider a mass-less infinite straight wire with one end fixed at O. Assume that the wire is rotating in a plane about the point O with constant angular velocity ω. Consider a bead of mass m sliding along the wire in the absence of external forces. Let r(t) denote the distance of the bead from O at time t ≥ 0, and \(\frac{dr}{dt}\)(0) = 0. Then which of the following statements is true?
1
∃M > 0, α > 0 such that r(t) > Meαt, t > 0
2
r(t) → 0 as t → ∞
3
r(t) is a constant function
4
\(\frac{dr(t)}{dt}\) changes its sign for some t > 0
5
Question Not Attempted