Two planet ratio of their radie is 1:2. ratio of their mass is2:7. Find the ratio of a body on these planets
Answers
Answer:
1:2
Explanation:As we learnt in
Acceleration due to gravity (g) -
Force extended by earth on a body is gravity.
Formula: g=\frac{GM}{R^{2}},
g=\frac{4}{3}\pi \rho \, GR
g\rightarrow gravity
\rho \rightarrow density of earth
R \rightarrow Radius of earth
- wherein
It's average value is 9.8\: m/s^{2}\; \; or \; \; 981cm/sec^{2}\; or\; 32feet/s^{2} on the surface of earth
\frac{g_{1}}{g_{2}}=\sqrt{\frac{M_{1}}{M_{2}}.\frac{R_{2}^{2}}{R_{1}^{2}}} =\sqrt{\frac{1}{2}.4}= \sqrt{2}
Option 1)
1 : 2
This is correct option
Option 2)
2 : 1
This is incorrect option
Option 3)
3 : 5
This is incorrect option
Option 4)
5 : 3
This is incorrect option
Explanation:
Let the ratio of radii be x.
Radius of 1st planet = x
Radius of 2nd planet = 2x
Let the ratio of masses be y.
Mass of 1st planet = 2y
Mass of 2nd planet = 7y
We know, gravity of planet is,
g = GM / r²
where G is the gravitational constant, M is the mass of planet and r is the radius of planet.
Gravity on first planet,
g = G×2y / x²
g = 2G.y/x²
Gravity on second planet,
g = G×7y / (2x)²
g = 7/4 G.y/x²
Ratio of gravity of first planet to second planet,
= 2 G.y x² / 7/4 G.y/x²
= 2 / 7/4
= 8/7
= 8:7
Let the ratio of gravity be z.
Gravity of first planet = 8z
Gravity of second planet = 7z
To find : Ratio of weight of body
We know, weight = m×g
Weight of body on 1st planet, = m×8z
= 8mz
Weight of body on 2nd planet, = m×7z
= 7mz
Ratio of weight of body =
8mz / 7mz
= 8:7
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