Question:

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

36^k

−34(^k−^i)

48(^i+^j)

−48^k

→L=m[→r×→v]
m=2kg
→r=2t^i−3t^2^j=4^i−12^j (At t = 2 sec)
→v=d→rdt=2^i−6t^j=2^i−12^j
→r×→v=(4^i−12^j)×(2^i−12^j)=−24^k
→L=m(→r×→v)=−48^k