Question 277: Centre of Mass and Rotational Motion

Question

The projectile motion of a particle of mass 5 g is shown in the figure.The initial velocity of the particle is $$5\sqrt 2 $$ ms-1 and the air resistance is assumed to be negligible. The magnitude of the change in momentum between the points A and B is x $$	imes$$ 10-2 kgms-1. The value of x, to the nearest integer, is __________.

Accepted Answer

$$|\overrightarrow u | = |\overrightarrow v |$$ .... (1)
$$\overrightarrow u  = u\cos 45\widehat i + u\sin 45\widehat j$$ ..... (2)
$$\overrightarrow v  = v\cos 45\widehat i - v\sin 45\widehat j$$ ..... (3)
$$|\Delta \overrightarrow P | = |m(\overrightarrow v  - \overrightarrow u )|$$ .... (4)
$$\Delta P = 2mu\sin 45^\circ $$
$$ = 2 	imes 5 	imes {10^{ - 3}} 	imes 5\sqrt 2  	imes {1 \over {\sqrt 2 }}$$
= 50 $$	imes$$ 10
$$-$$3
= 5 $$	imes$$ 10
$$-$$2

Centre of Mass and Rotational Motion

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