Question

If a body is projected with a speed lesser than escape velocity, then

• A. the body can reach a certain height and may fall down following a straight line path
• B. the body can reach a certain height and may fall down following a parabolic path
• C. the body may orbit the earth in a circular orbit
• D. the body may orbit the earth in an elliptical orbit

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A the body can reach a certain height and may fall down following a straight line path
B the body may orbit the earth in a circular orbit
C the body may orbit the earth in an elliptical orbit
D the body can reach a certain height and may fall down following a parabolic path

$\left(1\right)$ if $v<v_e$ and the body is projected vertically upwards, the body will rise up to that height where its velocity becomes zero. Afte rthat it will fall freely under force due to gravity following a straight line path.
$\left(2\right)$ If $v<v_e$ but the body is projected at some angle w.r.t. vertical direction, the body will reach upto a certain height (where vertical component of velocity becomes zero)and then fall down following n parabolic path. (This will be a case of projectile motion).
$\left(3\right)$ if $v=v_e=\sqrt{\frac{GM}{R}}$
then orbit will be circular.
$\left(4\right)$ But if $v_0<v<v_e$ (escape velocity) then orbit will be ellipse.
So all the options are correct.