An object is projected horizontally with speed 1 2 G M R , from a… - Vidyadip

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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