A particle of mass 2 kg is moving such that at time t, its position, in meter, is given by vecr(t)=5 hati-2t2 hatj. The angular momentum of the particle at t = 2s about the origin in kg m-2 s-1 is :

Question

A particle of mass 2 kg is moving such that at time t, its position, in meter, is given by vecr(t)=5 hati-2t2 hatj. The angular momentum of the particle at t = 2s about the origin in kg m-2 s-1 is : (A) -80 hatk (B) (10 hati-16 hatj) (C) -40 hatk (D) 40 hatk

Tardigrade Admin · Accepted Answer

Angular momentum L=m (v × r) =2 kg((dr/dt)× r)=2 kg (4t j × 5i - 2t2 hatj) =2 kg(-20 t hatk)==2 kg ×-20×2 m-2 s-1 hatk = -80 hatk

Q. A particle of mass $2 k g$ is moving such that at time $t$ , its position, in meter, is given by $r (t) = 5 \hat{i} - 2 t^{2} \hat{j}$ . The angular momentum of the particle at $t = 2 s$ about the origin in $k g m^{- 2} s^{- 1}$ is :

$- 80 \hat{k}$

$(10 \hat{i} - 16 \hat{j})$

$- 40 \hat{k}$

$40 \hat{k}$

Angular momentum $L = m (v \times r)$
$= 2 k g (\frac{d r}{d t} \times r) = 2 k g (4 t j \times 5 i - 2 t^{2} \hat{j})$
$= 2 k g (- 20 t \hat{k}) == 2 k g \times - 20 \times 2 m^{- 2} s^{- 1} \hat{k}$
= $- 80 \hat{k}$

Q. A particle of mass 2kg is moving such that at time t, its position, in meter, is given by r(t)=5i^−2t2j^​. The angular momentum of the particle at t=2s about the origin in kgm−2s−1 is :

−80k^

(10i^−16j^​)

−40k^

40k^