A projectile of mass "m" is projected from ground with a speed of… - Vidyadip

MCQ

$A$ projectile of mass $"m"$ is projected from ground with a speed of $50 \,m/s$ at an angle of $53^o$ with the horizontal. It breaks up into two equal parts at the highest point of the trajectory. One particle coming to rest immediately after the explosion. The ratio of the radii of curvatures of the moving particle just before and just after the explosion are:

✓
$1 : 4$
B
$1 : 3$
C
$2 : 3$
D
$4 : 9$

✓

Answer

Correct option: A.

$1 : 4$

a
At highest point the speed of broectle. Just he frue explosim.

$V=V \cos 53^{\circ} = 30\,m / s$

the explosim takes blare, ut the man of partice be $2 m$ from linear momentum conservation in $\{-a \times 1]$

$2 m \times 30= mv$

$v^{\prime}=60 m / s$

redius of currature just before pxploim

$\frac{2 m v^2}{\gamma}=2 m y$

$r^2 \frac{v^2}{r}=\frac{900}{10}=90\,m$

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