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Question

# The time dependence of the position of a particle of mass m =2 is given by →r(t)=2t^i−3t2^j. Its angular momentum, with respect to the origin, at time t=2 is :

A
36^k
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B
34(^k^i)
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C
48^k
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D
48(^i×^j)
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Solution

## The correct option is C −48^kGiven: mass m=2 time t=2 →r=2t^i−3t2^j Now, Position at time t=2 →r(at t=2)=(2×2)^i−(3×22)^j=4^i−12^j Velocity, →v=d→rdt=ddt(2t^i−3t2^j)=2^i−6t^j Velocity at time t=2 →v(at t=2)=2^i−(6×2)^j=2^i−12^j Now, angular momentum →L=mvr sinθ^n=m(→r×→v) =2(4^i−12^j)×(2^i−12^j)=−48^k Hence option (D) is correct.

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