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7. gravitation — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics7. gravitation1 Mark
MCQ
A solid cone is placed on a horizontal surface has height $h$, radius $R$ and apex angle $\theta$ as show.If gravitational potential energy of the cone does not change as position of the cone is changed from figure $(A)$ to figure $(B)$, then,
  • A
    $\theta  = {\sin ^{ - 1}}\left( {\frac{2}{3}} \right)$
  • B
    $\theta  = \frac{\pi }{4}$
  • C
    $\frac{h}{R} = 1$
  • ✓
    $\frac{h}{R} = 2\sqrt 2$
✓

Answer

Correct option: D.
$\frac{h}{R} = 2\sqrt 2$
d
Solid Cone

In $\triangle O C M$

$\sin \theta=\frac{h / 4}{3 h / 4}=\frac{1}{3}$

$\therefore \quad \tan \theta=\frac{1}{2 \sqrt{2}}=\frac{R}{h}$

$\therefore \quad \frac{\mathrm{h}}{\mathrm{R}}=2 \sqrt{2}$

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