A body of mass m is projected with a speed u making an angle of 45 o with the ground. The angular momentum of the body about the point of projection, at the highest point is expressed as 2 m u 3 X g .

Question

A body of mass m is projected with a speed u making an angle of 45 o with the ground. The angular momentum of the body about the point of projection, at the highest point is expressed as 2 m u 3 X g . The value of X is_______.

TestHub · Accepted Answer

Consider projection as shown in above diagram.

At the topmost point, velocity of the body will be $u \cos 45 °$ .

Therefore, we can write the required angular momentum as

$L = (m u_{H}) \times H = (m u \cos θ) (\frac{u^{2} \sin^{2} θ}{2 g})$

$= m u^{3} \times \frac{1}{4 \sqrt{2} g} \Rightarrow X = 8$

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