A bomb projected from ground at an angle , ( 90 ^o ) explodes int… - Vidyadip

MCQ

A bomb projected from ground at an angle $\theta \, \left( {\theta \ne {{90}^o}} \right)$ explodes into two fragments of equal mass at topmost point of it's trajectory. If one of the fragment returns to point of projection then ratio of De-broglie wavelength of second fragment just after explosion to bomb just before explosion is

A
$1$
B
$2$
✓
$\frac{2}{3}$
D
$\frac{3}{2}$

✓

Answer

Correct option: C.

$\frac{2}{3}$

c
from momentum conservation

$\operatorname{mucos} \theta=-\frac{\mathrm{m}}{2} \mathrm{u} \cos \theta+\frac{\mathrm{m}}{2} \mathrm{v}_{1}$

$\mathrm{v}_{1}=3 \mathrm{ucos} \theta$

$\lambda_{\mathrm{D}}=\frac{\mathrm{h}}{\mathrm{m} \mathrm{v}}$

$ \Rightarrow \frac{{\left( {{\lambda _{\rm{D}}}} \right)}}{{{{\left( {{\lambda _{\rm{D}}}} \right)}_2}}} = \frac{{\frac{{\rm{h}}}{{\frac{{\rm{m}}}{2}(3{\rm{u}}\cos \theta )}}}}{{\frac{{\rm{h}}}{{{\rm{mu}}\cos \theta }}}} = \frac{2}{3}$

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