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NEET 1998 (AIPMT) · Motion in a Plane (2-D Kinematics)

Motion in a Plane (2-D Kinematics) question from NEET 1998 (AIPMT)

Q26NEET 1998 · AIPMTMedium

Motion in a Plane (2-D Kinematics)

Two particles AA and BB are connected by a rigid rod ABAB. The rod slides along perpendicular rails as shown here. The velocity of AA to the right is 10 m/s10\text{ m/s}. What is the velocity of BB when angle α=60∘\alpha = 60^\circ?

Figure

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Answer: (c)

  1. Rod length fixed: x2+y2=L2⇒xdxdt+ydydt=0x^2 + y^2 = L^2 \Rightarrow x\frac{dx}{dt} + y\frac{dy}{dt} = 0
  2. ∣vB∣=vAxy=vAcot⁡α|v_B| = v_A\frac{x}{y} = v_A\cot\alpha
  3. ∣vB∣=10cot⁡60∘=103≈5.8|v_B| = 10\cot60^\circ = \frac{10}{\sqrt3} \approx 5.8 m/s (downward)
  4. So the answer is (c) 5.8 m/s.
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