The projectile motion of a particle of mass 5 , g is shown in the… - Vidyadip

MCQ

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 $x \times 10^{-2}\, kgms ^{-1} .$ The value of $x ,$ to the nearest integer, is ...... .

A
$10$
B
$8$
C
$3$
✓
$5$

✓

Answer

Correct option: D.

$5$

d
$|\overrightarrow{ u }|=|\overrightarrow{ v }|.....(1)$

$\overrightarrow{ u }=u \cos 45 \hat{ i }+ u \sin 45 \hat{ j }.....(2)$

$\overrightarrow{ v }= v \cos 45 \hat{ i }- v \sin 45 \hat{ j }.....(3)$

$|\overrightarrow{\Delta P }|=| m (\overrightarrow{ v }-\overrightarrow{ u })|.....(4)$

$\Delta P =2 mu \sin 45^{\circ}$

$=2 \times 5 \times 10^{-3} \times 5 \sqrt{2} \times \frac{1}{\sqrt{2}}$

$=50 \times 10^{-3}$

$=5 \times 10^{-2}$

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