First slide

Angular momentum

Question

A body of mass m is projected with vertical making an angle 45^o with the horizontal from the point P. Its highest point is H and it returns to the ground at Q. The change in angular momentum in going from P to Q is

Moderate

A

$\frac{4 {mv}^{3}}{g}$
B

$\frac{\sqrt{3} {mv}^{3}}{g}$
C

$\frac{{mv}^{3}}{\sqrt{2} g}$
D

$\frac{{mv}^{3}}{4 \sqrt{2} g}$

Solution

$| ΔL | = |L_{Q} - L_{P}| . Here L_{P} = 0$
$∴ ΔL = L_{Q} = r \times p = R \times p$
where r = R = range
At an angle of $45^{\circ}$
$\begin{array}{l} R = \frac{V^{2}}{g} and p = musin 45^{\circ} = \frac{mu}{\sqrt{2}} \\ ∴ ΔL = \frac{V^{2}}{g} \times \frac{mv}{\sqrt{2}} = \frac{{mv}^{3}}{\sqrt{2} g} \end{array}$

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