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5.work,energy,power and collision — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysics5.work,energy,power and collision1 Mark
MCQ
A particle $A$ is projected vertically upwards. Another particle $B$ is projected at an angle of $45^{\circ}$. Both reach the same height. The ratio of the initial kinetic energy of $A$ to that of $B$ is
  • ✓
    $1 : 2$
  • B
    $2 : 1$
  • C
    $1\,\,:\,\,\sqrt 2 $
  • D
    $\sqrt 2 \,\,:\,\,1$
✓

Answer

Correct option: A.
$1 : 2$
a
$\frac{{v_1^2}}{{2g}}\,\, = \,\,\frac{{v_2^2\,\,{{\sin }^2}\,\,45}}{{2g}}\,\,\,\,\therefore \,\,\,\,v_1^2\,\, = \,\,\frac{{v_2^2}}{2}$

$\frac{{{K_1}}}{{{K_2}}}\,\, = \,\,\frac{{\frac{1}{2}\,\,mv_1^2}}{{\frac{1}{2}\,\,mv_2^2}}\,\, = \,\,\frac{{v_1^2}}{{v_2^2}}\,\, = \,\,\frac{1}{2}$

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