A particle of mass $M$ is situated at the centre of a spherical shell of same mass and radius $a$. The gravitational potential at a point situated at $\frac{a}{2}$ distance from the centre, will be

The dependence of acceleration due to gravity $g$ on the distance $r$ from the centre of the earth assumed to be a sphere of radius $R$ of uniform density is as shown figure below

The correct figure is

The escape velocity of a body from earth's surface is $v_e$ . The escape velocity of the same body from a height equal to $R$ from the earth's surface will be

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 satellite $S$ is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Then

The variation of acceleration due to gravity $g$ with distance $d$ from centre of the earth is best represented by ($R =$ Earth's radius)