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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 ball is projected vertically upwards with a certain initial speed. Another ball of the same mass is projected with the same speed at an angle of $30^o$ with the horizontal. At the highest point, the ratio of their potential energies is
  • A
    $1:1$
  • B
    $2:1$
  • C
    $3:2$
  • ✓
    $4:1$
✓

Answer

Correct option: D.
$4:1$
d
The first ball reaches to a maximum height

$\mathrm{h}=\frac{\mathrm{u}^{2}}{2 \mathrm{g}}$

$\left(using\, v^{2}=u^{2}-2 g h\right)$

The second ball attains the maximum height

$\mathrm{h}^{\prime}=\frac{\mathrm{u}^{2} \sin ^{2} .30^{\circ}}{2 \mathrm{g}}=\frac{1}{4}\left(\frac{\mathrm{u}^{2}}{2 \mathrm{g}}\right)$

$\frac{\text { Potential energy of first ball }}{\text { Potential energy of sec ond ball }}=\frac{\operatorname{mgh}}{\operatorname{mgh}^{\prime}}=\frac{h}{h^{\prime}}=\frac{4}{1}$

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