Question

In a conical pendulum, a bob of mass m, moves in horizontal circle, with constant speeds v, with help of a string of length l as shown in figure. The angular momentum of particle about the S will be

• A. $\mathrm{mv}\ell [\cos \theta \hat{i}+\sin \theta \hat{j}]$
• B. $\mathrm{mvl}[\sin \theta \hat{i}+\cos \theta \hat{j}]$
• C. $\mathrm{mvt}[-\cos \theta \hat{i}+\sin \theta \hat{j}]$
• D. $mv\ell [\cos \theta \hat{i}-\sin \theta \hat{j}]$

Answer 1

The correct option is A $\mathrm{mv}\ell [\cos \theta \hat{i}+\sin \theta \hat{j}]$

$\begin{array}{cc}\text{Angular momentum}L=I\omega & \\ & =m{l}^2\times \frac{v}{l}[\cos \theta \hat{i}+\sin \theta \hat{j}]\\ & =mvl[\cos \theta \hat{i}+\sin \theta \hat{j}]\end{array}$