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JEE Main 2026 (2 Apr, Shift 1) · Angular Momentum & its Conservation

Angular Momentum & its Conservation question from JEE Main 2026 (2 Apr, Shift 1)

Q4JEE Main 2026 · 2 APR · SHIFT 1Medium

Angular Momentum & its Conservation

The position of an object having mass 0.1 kg as a function of time tt is given as

r⃗=(10t2i^+5t3j^)\vec{r} = \left(10t^{2}\hat{i} + 5t^{3}\hat{j}\right) m. At t=1t = 1 s, which of the following statements are correct? A. The linear momentum p⃗=(2i^+1.5j^)\vec{p} = \left(2\hat{i} + 1.5\hat{j}\right) kg·m/s.

B. The force acting on the object F⃗=(2i^+3j^)\vec{F} = \left(2\hat{i} + 3\hat{j}\right) N.

C. The angular momentum of the object about its origin L⃗=15k^\vec{L} = 15\hat{k} J·s.

D. The torque acting on the object about its origin τ⃗=20k^\vec{\tau} = 20\hat{k} N·m.

Choose the correct answer from the options given below:

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Answer: (d)

  1. v⃗=20ti^+15t2j^\vec v=20t\hat i+15t^2\hat j, a⃗=20i^+30tj^\vec a=20\hat i+30t\hat j. At t=1t=1: r⃗=10i^+5j^\vec r=10\hat i+5\hat j, v⃗=20i^+15j^\vec v=20\hat i+15\hat j, a⃗=20i^+30j^\vec a=20\hat i+30\hat j.
  2. A: p⃗=0.1v⃗=2i^+1.5j^\vec p=0.1\vec v=2\hat i+1.5\hat j — correct.
  3. B: F⃗=0.1a⃗=2i^+3j^\vec F=0.1\vec a=2\hat i+3\hat j N — correct.
  4. C: L⃗=r⃗×p⃗=(10×1.5−5×2)k^=5k^\vec L=\vec r\times\vec p=(10\times1.5-5\times2)\hat k=5\hat k, not 15k^15\hat k — wrong.
  5. D: τ⃗=r⃗×F⃗=(10×3−5×2)k^=20k^\vec\tau=\vec r\times\vec F=(10\times3-5\times2)\hat k=20\hat k — correct.
  6. So the answer is (d) A, B and D only.
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