A body moves in a circle of radius R having centre at origin, with an angular velocity w in the x-y plane as shown in the figure. Another body moves parallel to y-axis with constant velocity (Rω/2). At time t = 0, both particles are at (R, 0). The value time t, when first body has velocity only along positive x-axis w.r.t. the second body is

Engineering

Physics

Relative Motion

Calculus

Circular Motion in Vertical Plane

Question

A body moves in a circle of radius R having centre at origin, with an angular velocity w in the x-y plane as shown in the figure. Another body moves parallel to y-axis with constant velocity (Rω/2). At time t = 0, both particles are at (R, 0). The value time t, when first body has velocity only along positive x-axis w.r.t. the second body is

5π/(3ω)

π/(6ω)

5π/(6ω)

None

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(v_y)_rel. = 0
$∴$ Rω cos θ = $\frac{Rω}{2}$
θ = $\frac{π}{3}$
$∴$ Angular displacement of the second body = 2π – $\frac{π}{3}$
$∴$ ωt = $\frac{5 π}{3}$
t = $\frac{5 π}{3 ω}$