The variation of velocity of a particle executing SHM with time is shown in figure. The velocity of the particle when a phase change of $\pi /6$ takes place from the instant it is at one of the extreme positions will be 

detailed solution

Correct option is B

From the graph T = (5 -1) = 4 s(distance between the two adjacent crests shown in the figure)and vmax=5m/s; ωA=5m/s2πTA=5⇒A=5T2π=5×42π=10πmAlso, ω=2π4=π2rad/sThe equation of velocity can be written asv=5sin⁡π2tm/s At extreme position, v=0;sin⁡π2t=0  or  t=2sPhase of the particle velocity at that instant correspondingto the above equation = π.Therefore, when a phase change of π/6 takes place, theresulting phase = π+π/6.v=5sin⁡π+π6=−5sin⁡π6=−512=2.5m/s (numerically)