The radius and mass of the Earth are both increased by $0.5\%$. Which of the following statements is true at the surface of the Earth?

$A$ large spherical mass $M$ is fixed at one position and two identical point masses $m$ are kept on a line passing through the centre of $M$ (see figure). The point masses are connected by a rigid massless rod of length $\ell$ and this assembly is free to move along the line connecting them. All three masses interact only through their mutual gravitational interaction. When the point mass nearer to $M$ is at a distance $r = 3\ell$ from $M$,the tension in the rod is zero for $m = k\left(\frac{M}{288}\right)$. The value of $k$ is

What is the gravitational force exerted by the sphere of mass $M$ and radius $a$ on a ring of mass $m$ and radius $a$,where the distance between the center of the ring and the center of the sphere is $r = 1.73a = \sqrt{3}a$?

$A$ tunnel is dug in the Earth across one of its diameters. Two masses $m$ and $2m$ are dropped from the ends of the tunnel. The masses collide, stick to each other, and perform $S.H.M.$ The amplitude of the $S.H.M.$ will be:

If the height of a satellite from the surface of the Earth is increased,then its

$A$ planet is moving in an elliptical orbit around the sun. The work done on the planet by the gravitational force of the sun:
$(i)$ is zero in no part of the motion.
(ii) is zero in some parts of the orbit.
(iii) is zero in one complete revolution.
(iv) is zero in any small part of the orbit.
Which of the following is true?