The orbital velocity of an artificial satellite in a circular orbit very close to earth is $v$. The velocity of a geo-stationary satellite orbiting in circular orbit at an altitude of $3R$ from earth's surface will be
$\frac{v}{{\sqrt 7 }}$
$\frac{v}{{\sqrt 6 }}$
$\frac{v}{2}$
$\frac{v}{{\sqrt 2 }}$
A rocket of mass $M$ is launched vertically from the surface of the earth with an initial speed $V.$ Assuming the radius of the earth to be $R$ and negligible air resistance, the maximum height attained by the rocket above the surface of the earth is
A small ball of mass $'m'$ is released at a height $'R'$ above the Earth surface, as shown in the figure. If the maximum depth of the ball to which it goes is $R/2$ inside the Earth through a narrow grove before coming to rest momentarily. The grove, contain an ideal spring of spring constant $K$ and natural length $R,$ the value of $K$ is ( $R$ is radius of Earth and $M$ mass of Earth)
Which of the following statements are true about acceleration due to gravity?
$(a)\,\,'g'$ decreases in moving away from the centre if $r > R$
$(b)\,\,'g'$ decreases in moving away from the centre if $r < R$
$(c)\,\,'g'$ is zero at the centre of earth
$(d)\,\,'g'$ decreases if earth stops rotating on its axis
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)
At what altitude will the acceleration due to gravity be $25\% $ of that at the earth’s surface (given radius of earth is $R$) ?