JEE Main202522 Jan 2025Morning ShiftPhysicsRotational MotionActual
The position vectors of two 1 kg particles, (A) and (B), are given by r _ A = ( ₁ t ^2 i + ₂ t j + ₃ t k ) m and r _ B = ( ₁ t i + ₂ t ^2 j + ₃ t k ) m , respectively; ( ₁=1 ~m / s ^2, ₂=3 n m / s , ₃=2 ~m / s , ₁=2 ~m / s , ₂=-1 ~m / s ^2, ₃=4 pm / s ) , where t is time, n and p are constants. At t=1 ~s , | V_A |= | V _B | and velocities V _A and V _B of the particles are orthogonal to each other. At t=1 ~s , the ma
Correct answer
0
Step-by-step solution
At t=1r_ A B =-1 i +(3 n+1) j +(2-4 p) k At t=1 aligned & v_A=2 i +3 n j +2 k & v_B=2 i -2 j +4 p k & v _A- v _B=0, 4-6 n+8 p=0 aligned gathered |v_A |= |v_B | (3 n)^2+4=4+16 p^2 3 n=-4 p 4+16 p=0 p=- 1 4 , n= 1 3 r_ A B =- i +2 j +3 k v_A=2 i + j +2 k L=m | r _ A B v _A |=90 gathered