Question 280: 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 __________.
![](https://imagex.cdn.examgoal.net/1kmnl50ay/c9012ac4-c144-4360-adb1-101a174f3fa4/489522a0-8cb3-11eb-bb7d-75e16383db04/file-1kmnl50az.jpg)

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
![](https://imagex.cdn.examgoal.net/1kmp8zjhy/cf617a22-6ffc-4ad2-9e03-822e6bdd520f/544dd160-8d9d-11eb-ac14-9b8a8da3c92c/file-1kmp8zjhz.png)

Centre of Mass and Rotational Motion

Integer / Numeric Answer Type