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7. gravitation — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysics7. gravitation1 Mark
MCQ
An object is projected horizontally with speed $\frac{1}{2} \sqrt{\frac{G M}{R}}$, from a point at height $3 R$ [where $R$ is radius and $M$ is mass of earth, then object will] 
  • A
    Fall back on surface of earth by following parabolic path
  • B
    Fall back on surface of earth by following hyperbolic path
  • ✓
    Start rotating around earth in a circular orbit
  • D
    Escape from gravitational field of earth
✓

Answer

Correct option: C.
Start rotating around earth in a circular orbit
c
(c)

At height $3 R$, i.e at distance $4 R$ from the centre of the earth,

$V_{\text {orbital }}=\sqrt{\frac{G M}{r}}$

Here, $r=4 R \Rightarrow V_0=\sqrt{\frac{G M}{4 R}}=\frac{1}{2} \sqrt{\frac{G M}{R}}$,

Thus, an object taken to a height $3 R$ if projected horizontally with speed $\frac{1}{2} \sqrt{\frac{G M}{R}}$, will start rotating around earth in a circular orbit.

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