A particle of mass 100 g is projected at time with a speed at an angle to the horizontal as given in the figure. The magnitude of the angular momentum of the particle about the starting point at time is found to be . The value of is _________ . (Take

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Solution

Q.
A particle of mass 100 g is projected at time $t = 0$ with a speed $20 {ms}^{- 1}$ at an angle $45 °$ to the horizontal as given in the figure. The magnitude of the angular momentum of the particle about the starting point at time $t = 2 s$ is found to be $\sqrt{K} {kgm}^{2} /s$ . The value of $K$ is _________ . (Take $g = 10 {ms}^{- 2}$ ) [2023]

Ans.
(800)

$Use Δ L = \int_{0}^{t} τ d t$

$L_{0} = \int_{0}^{2} m g (v_{x} t) d t$

$= m g v_{x} \frac{t^{2}}{2} = (0.1) (10) (10 \sqrt{2}) \frac{2^{2}}{2} = 20 \sqrt{2}$

$= \sqrt{800} {kg m}^{2} / s$

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