Question

a mass of 2400 kg is placed on planet whose mass is ⅙ of that of earth and radius is 2 times of earth then take g-9.8m/s²​

Answer 1

Correct Question :

A mass of 2400kg is placed on another planet whose mass is ⅙ of that of earth and radius is 2 times of earth. Find weight of object on that planet. (Take g = 9.8 m/s²)

Solution :

❖ Gravitational acceleration of a planet of mass m and radius r is given by

$\dag\:\underline{\boxed{\bf{\gray{g=\dfrac{GM}{R^2}}}}}$

Where G denotes gravitational constant

First of all we need to find acceleration die to gravity of another planet.

$\sf:\implies\:\dfrac{g}{g'}=\dfrac{M}{M'}\times\dfrac{R'^2}{R^2}$

• M' = M/6
• R' = 2R

$\sf:\implies\:\dfrac{9.8}{g'}=\dfrac{M}{M/6}\times\dfrac{(2R)^2}{R^2}$

$\sf:\implies\:\dfrac{9.8}{g'}=6\times 4$

$\sf:\implies\:g'=\dfrac{9.8}{24}$

$\bf:\implies\:g'=0.408\:ms^{-2}$

❖ Weight of object :-

Weight of object on any planet is measured as the product of mass and acceleration due to gravity.

➙ W = m × g'

➙ W = 2400 × 0.408

➙ W = 979.2 N

Answer 2

The weight of the object on the planet will be 979.2 N.

Step-by-step procedure

Although a part of your question is missing, you might be referring to this full question:

"A mass of 2400kg is placed on another planet whose mass is ⅙ of that of earth and radius is 2 times of The earth. Find the weight of an object on that planet. "

Given:

Let the mass and radius of the earth be M and R respectively. Let its gravitational acceleration be g.

Mass of object = 2400 kg

Mass of the planet, M' = 1/6 M

Radius of the planet; r'= 2r

We know from the formula for gravitational acceleration:

g(Earth) = GM/ $r^{2}$

g'(planet)= G x 1/6M/$(2r)^{2}$

Dividing g and g' :

g/g'= M x  $r^{2}$÷M/6 X $(2r)^{2}$

So, 9.8/g'= 6 x 4

g'= 9.8 ÷24 = 0.408 m/$s^{2}$

Now, we know

weight = mass x gravitational acceleration

so, weight= 2400 x 0.408 =979.2 N

Result:

Thus, the weight of the object on planet will be 979.2 N.

(#SPJ3)