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7. gravitation — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics7. gravitation1 Mark
MCQ
An object is projected vertically up from the earth's surface with velocity $\sqrt {Rg}$ where $R$ is the radius of the earth and $'g'$ is the acceleration due to earth on the  surface of earth. Find the maximum height reached by the object.
  • A
    $\frac{R}{2}$
  • ✓
    $R$
  • C
    $2R$
  • D
    $3R$
✓

Answer

Correct option: B.
$R$
b
Let the object of mass $\mathrm{m}$ projected with speed

$\mathrm{u}=\sqrt{\mathrm{Rg}}$ reach a height $'h'$ above surface of

earth.

Then from conservation of energy

$\frac{1}{2} m u^{2}-\frac{G M m}{R}=-\frac{G M m}{R+h}$

$\mathrm{u}^{2}=\mathrm{g} \mathrm{R}=\frac{\mathrm{GM}}{\mathrm{R}}$

$\Rightarrow \frac{1}{2} \frac{\mathrm{GMm}}{\mathrm{R}}-\frac{\mathrm{GMm}}{\mathrm{R}}=-\frac{\mathrm{GMm}}{\mathrm{R}+\mathrm{h}}$ or $\mathrm{h}=\mathrm{R}$

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