A projectile is projected with velocity $k{v_e}$ in vertically upward direction from the ground into the space. (${v_e}$ is escape velocity and $k < 1)$. If air resistance is considered to be negligible then the maximum height from the centre of earth to which it can go, will be : (R = radius of earth)
$\frac{R}{{{k^2} + 1}}$
$\frac{R}{{{k^2} - 1}}$
$\frac{R}{{1 - {k^2}}}$
$\frac{R}{{k + 1}}$
The condition for a uniform spherical mass m of radius r to be a black hole is [ $G$ = gravitational constant and $g$ = acceleration due to gravity]
The value of escape velocity on a certain planet is $2\, km/s$ . Then the value of orbital speed for a satellite orbiting close to its surface is
Which of the following graph represents the variations of acceleration due to gravity $(g)$ with distance $r$ from the centre of earth?
Given that mass of the earth is $M$ and its radius is $R$. A body is dropped from a height equal to the radius of the earth above the surface of the earth. When it reaches the ground its velocity will be
If the radius of the earth were shrink by $1\%$ and its mass remaining the same, the acceleration due to gravity on the earth's surface would