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3.2 , motion in plane — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics3.2 , motion in plane1 Mark
MCQ
A particle $A$ is projected vertically upwards. Another identical particle $B$ is projected at an angle of $45^o $ . 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
Let the speed of $A$ and $B$ are $v_{1}$ and $v_{2}$,

Given, their maximum heights are equal$:$

$\frac{v_{1}^{2}}{2 g}=\frac{v_{2}^{2} \sin ^{2} 45}{2 g}$

$\Rightarrow v_{1}^{2}=\frac{v_{2}^{2}}{2}$

$\frac{K_{1}}{K_{2}}=\frac{\frac{1}{2} m v_{1}^{2}}{\frac{1}{2} m v_{2}^{2}}=\frac{v_{1}^{2}}{v_{2}^{2}}=\frac{1}{2}$

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