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JEE Main 2026 (6 Apr, Shift 1) · Critical Speed & Looping

Critical Speed & Looping question from JEE Main 2026 (6 Apr, Shift 1)

Q3JEE Main 2026 · 6 APR · SHIFT 1Medium

Critical Speed & Looping

A smooth inclined plane ends in a vertical circular loop, as shown in the figure. A small body is released from height hh as shown. If the body exerts a force of three times its weight on the plane at the highest point of circle then the height h=αRh = \alpha R. The value of α\alpha is ______

Figure

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Answer: (b)

  1. At the top: N+mg=mv2RN + mg = \frac{mv^2}{R} with N=3mg⇒v2=4gRN = 3mg \Rightarrow v^2 = 4gR
  2. Top of loop is at height 2R2R: mgh=mg(2R)+12m(4gR)mgh = mg(2R) + \frac{1}{2}m(4gR)
  3. h=2R+2R=4R⇒α=4h = 2R + 2R = 4R \Rightarrow \alpha = 4
  4. So the answer is (b) 4.
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