The positon vector r → of a particle of mass m is given by the following equation r → t = α…

The positon vector r→ of a particle of mass m is given by the following equation r→t=αt3i^+βt2j^, where α=103 ms-3, β=5 ms-2 and m=0.1 kg. At t=1s, which of the following statements (s) is (are) true about the particle?
  1. The velocity v→ is given by v→=10i^+10j^ ms-1
  2. The angular momentum L→ with respect to the origin is given by L→=-53k^ Nms
  3. The force F→ is given by F→=i^+2j^N
  4. The torque τ→ with respect to the origin is given by τ→=-203k^ Nm 

Solution

r→=αt3i^+βt2j^
v→=dr→dt=3αt2i^+2βtj^
a→=d2r→dt2=6αti^+2βj^
At t = 1
(i) v→=3×103×1i^+2×J×1j^
=10i^+10j^
(ii) L→=r→×p→
=103×1i^+5×1j^×0.110i^+10j^
= -53k^ 
(iii) F→=m×6×103×1i^+2×5j^=2i^+j^
(iv) τ→=r×F→
=103i^+5j^×2i^+j^
=+103k^+10-k^
=-203k^  ^

Asked in: JEE Advanced 2016 (Paper 1)

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