During the motion of a planet from perihelion to aphelion,the work done by the gravitational force of the sun on it is ...........

$Assertion$ : The Earth is slowing down and as a result the Moon is coming nearer to it.
$Reason$ : The angular momentum of the Earth-Moon system is not conserved.

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?

Assume that a tunnel is dug along a chord of the Earth,at a perpendicular distance $(R / 2)$ from the Earth's centre,where $R$ is the radius of the Earth. The wall of the tunnel is frictionless. If a particle is released in this tunnel,it will execute a simple harmonic motion with a time period:

State whether the following statements are true or false:
$(a)$ The value of acceleration due to gravity increases as we go to a depth $d$ below the Earth's surface.
$(b)$ If the escape velocity for an object of mass $m$ on the Earth's surface is $11.2 \, km/s$,then the escape velocity for an object of mass $2m$ is $22.4 \, km/s$.
$(c)$ If the Earth's gravitational attraction suddenly disappears,the mass of an object becomes zero,but its weight remains the same.

Two particles of equal mass $(m)$ each move in a circle of radius $(r)$ under the action of their mutual gravitational attraction. Find the speed of each particle.