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  4. 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 √ K kg m 2 / s. The value of K is (Take g=10 ms -2 )

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Q. A particle of mass $100 \,g$ is projected at time $t=0$ with a speed $20 \,ms ^{-1}$ at an angle $45^{\circ}$ 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 $\sqrt{ K } \,kg\, m ^2 / s$. The value of $K$ is __
(Take $g=10 \,ms ^{-2}$ )Physics Question Image

JEE MainJEE Main 2023System of Particles and Rotational Motion

Solution:

Use $\Delta L =\int\limits_0^t \tau d t$
$ L _0=\int\limits_0^2 mg \left( v _{ x } t \right) dt $
$ = mgv _{ x } \frac{ t ^2}{2}=(0.1)(10)(10 \sqrt{2}) \frac{2^2}{2} $
$ =20 \sqrt{2} $
$ =\sqrt{800}\, kg\, m ^2 / s$