A uniform rod has mass m = 2 kg and length ℓ = 13 m . One end of the rod is pulled with a constant velocity of v 0 = 34 m / s along a frictionless horizontal floor in the negative x direction. The o

Question

A uniform rod has mass m = 2 kg and length ℓ = 13 m . One end of the rod is pulled with a constant velocity of v 0 ​ = 34 m / s along a frictionless horizontal floor in the negative x direction. The other end is moving along a parabolic fixed curve. The equation of the parabola is x 2 = 20 y . Find the angular velocity of the rod (in rad/s) when the end point ' B ' is at ( 10 , 5 )

TestHub · Accepted Answer

Rod 5-12-13 at this instant: sin α = 13 5 ​ , cos α = 13 12 ​ ; parabola slope at B(10,5): tan θ = d x d y ​ = 10 x ​ = 1 , so θ = 4 5 ∘ and β = θ − α . Rigid-rod constraint: v 0 ​ cos α = v B ​ cos β ⇒ v B ​ = c o s 22.3 8 ∘ 34 × 12/13 ​ = 33.94 m/s. ω = ℓ v 0 ​ s i n α + v B ​ s i n β ​ = 13 13.08 + 12.92 ​ = 2 rad/s

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JEE Advanced 2027 (Class 12+)