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JEE Main 2026 · 2 Apr · Shift 1, Physics question 29

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 :

Choose one option
Answer and worked solution

Official answer: D

Kinematics at t = 1 s. v⃗=(20t,15t2)=(20,15)\vec v=(20t,15t^2)=(20,15) and a⃗=(20,30t)=(20,30)\vec a=(20,30t)=(20,30).

  • A: p⃗=0.1v⃗=(2,1.5)\vec p=0.1\vec v=(2,1.5) ✓
  • B: F⃗=0.1a⃗=(2,3)\vec F=0.1\vec a=(2,3) ✓
  • C: L⃗=r⃗×p⃗=(10)(1.5)−(5)(2)=5k^\vec L=\vec r\times\vec p=(10)(1.5)-(5)(2)=5\hat k ✗
  • D: τ⃗=r⃗×F⃗=(10)(3)−(5)(2)=20k^\vec\tau=\vec r\times\vec F=(10)(3)-(5)(2)=20\hat k ✓

A, B and D.

(D)

Topics:Angular momentum and its conservationTorque and rotational dynamicsNewton's laws
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