Question

The radius of a planet A is twice that of planet B. The average density of the material of planet A is thrice that of planet B. The ratio between the values of acceleration due to gravity on the surface of planet A and that on the surface of planet B is:
(A) $\dfrac{2}{3}$
(B) $\dfrac{3}{2}$
(C) $\dfrac{4}{3}$
(D) $6$

Answer 1

We know that freefall is a special case of motion with constant acceleration, because acceleration due to gravity is always constant and downward. This is true even when an object is thrown upward or has zero velocity. Acceleration from gravity is always constant and downward, but the direction and magnitude of velocity change. The acceleration due to gravity is always negative. Any object affected only by gravity (a projectile or an object in free fall) has an acceleration of$-9.81\text{ }m/{{s}^{2}}$, regardless of the direction. The acceleration is negative when going up because the speed is decreasing.

Complete step-by step answer:
We know that since g is calculated using only constants, g is a constant. where Re is the radius of the earth. As earth is not a perfect sphere, the value of gravity g is not a constant at all the locations on the surface of the earth. Therefore, for practical purposes we take acceleration due to gravity as a constant.
Acceleration due to gravity at planet’s surface $g=\dfrac{GM}{{{R}^{2}}}$
Mass of the planet $M=pV=p\dfrac{4}{3}\pi {{R}^{3}}$
$\Rightarrow g\dfrac{4}{3}\pi GpR$
Or, $\dfrac{{{g}_{A}}}{{{g}_{B}}}=\dfrac{{{p}_{A}}{{R}_{A}}}{{{P}_{B}}{{R}_{B}}}$
Given, ${{\rho }_{A}}={{3}_{\rho B}}\,and\,{{R}_{A}}=2R{{E}_{B}}$
$\therefore \dfrac{{{g}_{A}}}{{{g}_{B}}}=\dfrac{3{{\rho }_{B}}\left( 2{{R}_{B}} \right)}{{{\rho }_{B}}{{R}_{B}}}=6$

Hence, the correct answer is Option D.

Note: We know that acceleration is the velocity increasing or decreasing (dependent direction of acceleration) in 1 second. So, at maximum height velocity becomes zero. then acceleration still acts on the object and there is no balancing force at maximum height which can hold the object at max height. an object in constant acceleration has a linear velocity vs. time graph; that is, the slope of the graph is constant. Initial velocity is independent of the slope of the graph; that is, the acceleration. An object thrown downward still accelerates after release at the same rate as an object that is dropped.
It is known to us that sometimes an accelerating object will change its velocity by the same amount each second. This is referred to as a constant acceleration since the velocity is changing by a constant amount each second. An object with a constant acceleration should not be confused with an object with a constant velocity.