Question

The diameters of two planets are in ratio \[4:1\]their mean densities
have ratio \[1:2\]. The ratio of gravitational acceleration on the surface
of planets will be:
A. \[1:2\]
B. \[1:4\]
C. \[2:1\]
D. \[4:1\]

Answer 1

Hint:Any article situated in the field of the earth encounters a gravitational draw. Gravitational speeding up is portrayed as the item getting an increasing speed because of the power of gravity following up on it.
Gravitational speeding up is an amount of vector that has both size and heading.

Formula used
$g = \dfrac{3}{2}\pi GD\rho $
Here, \[g\] is consistently $9.8m/{s^2}$, simply increase the article's mass by $9.8$ and we will get its power of gravity.

Complete step by step answer:
The diameters of first planet $ = 4$
The diameters of second planet $ = 1$
Their mean densities have ratio $1$ and $2$
We need to find a acceleration on the surface of planets will be:
Let ${g_1}$ be $\left( {{D_1},{\rho _1}} \right)$ and ${g_2}$ be $\left( {{D_2},{\rho _2}} \right)$
Here the values are ${D_1} = 4$ and ${D_2} = 2$
Also, the values are ${\rho _1} = 1$ and${\rho _2} = 2$
Putting into the formula and we get,
${g_2}{g_1} = \dfrac{{{D_1}{\rho _{_1}}}}{{{D_2}{\rho _{{2_{}}}}}}$
$ = \dfrac{4}{1} \times \dfrac{1}{2}$
On cancelling the term and we get,
$ \Rightarrow \dfrac{2}{1}$
Now we have to put into the ratio as,
\[ \Rightarrow 2:1\]

Hence the correct option is $\left( C \right)$

Additional information:
Compute your neighborhood gravity, Divide your nearby gravity by standard gravity, and multiply your estimation result by your gravity rectification factor.

Gravity is a power that draws in objects toward the Earth.

It is an estimate of the gravitational power that draws in objects of mass toward one another at significant stretches. The condition likewise shows the heaviness of an item \[\left( {W = mg} \right)\].
The significant element of this power is that all items fall at a similar rate, paying little heed to their mass.

Note:For confirmation that the gravitational power approaches the power of gravity for objects near Earth, see Gravity Constant Factors.
Gravity of the Moon and on different planets has various estimations of the quickening because of gravity.

Notwithstanding, the impacts of the power are comparable.

There is frequently disarray concerning the assignment of weight and mass. Albeit a kilogram should be a unit of mass, it is frequently used to assign weight.
You should know that weight \[1{\text{ }}kg\] of mass is \[W = 9.8\] newton’s.