The rotation of the earth having radius $R$ about its axis speeds upto a value such that a man at latitude angle $60^{\circ}$ feels weightless. The duration of the day in such case will be:

$Assertion$ : The length of the day is slowly increasing.
$Reason$ : The dominant effect causing a slowdown in the rotation of the earth is the gravitational pull of other planets in the solar system.

The ratio of gravitational acceleration at height $3R$ to that at height $4R$ from the surface of the earth is : (where $R$ is the radius of the earth)

A projectile is fired from the surface of the earth with a velocity of $5\, ms^{-1}$ and angle $\theta$ with the horizontal. Another projectile fired from another planet with a velocity of $3\, ms^{-1}$ at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (in $ms^{-2}$) is (given $g = 9.8\, m/s^2$)

If the radius of the earth were to shrink by $1\%$ its mass remaining the same, the acceleration due to gravity on the earth's surface would

Write the difference between $G$ and $g$.