A conical pendulum consists of a mass M suspended from a strong sling of length l. The mass executes a circle of radius R in a horizontal plane with speed v. At time t, the mass is at position $R \hat{i}$ and has $v \hat{j}$ velocity. At time t, the angular momentum vector of mass M about the point from which the string passes on the ceiling is

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$Mvl \hat{k}$

$MvR \hat{k}$

$Mvl [\sqrt{\frac{l^{2} - R^{2}}{l}} \hat{i} + \frac{R}{l} \hat{k}]$

$- Mvl [\sqrt{\frac{l^{2} - R^{2}}{l}} \hat{i} + \frac{R}{l} \hat{k}]$

answer is C.

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Detailed Solution

From the figure in question, position vector of mass

$\vec{r} = R \hat{i} - \sqrt{l^{2} - R^{2} \hat{k}}$

Linear moment $\vec{p} = Mv \hat{j}$

$\vec{L} = \vec{r} \times \vec{p}$

Substituting the values, we get result (3)

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