A person whose mass is $100\, {kg}$ travels from Earth to Mars in a spaceship. Neglect all other objects in sky and take acceleration due to gravity on the surface of the Earth and Mars as $10$ ${m} / {s}^{2}$ and $4 \,{m} / {s}^{2}$ respectively. Identify from the below figures, the curve that fits best for the weight of the passenger as a function of time.

If the Earth has no rotational motion, the weight of a person on the equator is $W$. Determine the speed with which the earth would have to rotate about its axis so that the person at the equator will weight $\frac{3}{4}\,W$ . Radius of the Earth is $6400\, km$ and $g = 10\, m/s^2$

If all objects on the equator of earth feel weightless then the duration of the day will nearly become ……. $hr$

At what height above the earth’s surface does the acceleration due to gravity fall to $1\%$ of its value at the earth’s surface ?

$Assertion$ : Space rocket are usually launched in the equatorial line from west to east
$Reason$ : The acceleration due to gravity is minimum at the equator.