Physics, 28.12.2019 04:31 gui00g7888888888888

Anew planet is discovered that has twice the earth's mass and twice the earth's radius. on the surface of this new planet a person who weights 500 n on earth would experience a gravitational force of
a. 125 n
b. 250 n
c. 500 n
d. 1000 n
e. 2000 n

Answers: 1

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To solve this problem we will proceed to use the expression of gravity given in Newtonian theory in terms of mass, the radius the universal gravitational constant, that is:

$g = \frac{GM}{R^2}$

This expression defines as gravity on earth. On another planet with twice the mass and radius constants it would be given as,

$g' = \frac{G2M}{(2R)^2}$

$g' = \frac{2GM}{4R^2}$

$g' = \frac{1}{2} *\frac{GM}{R^2}$

$g' = \frac{g}{2}$

Expressing the weight of the planet this would be then

W = mg'

$W = m\frac{g}{2}$

$W = \frac{500N}{2}$

W = 250N

Correct answer is B.

Answer from: nnaaatt1845

The weight of person on the new planet is of 250 N. Hence, option (c) is correct.

Given data:

The weight of person on Earth is, W = 500 N.

The standard expression for the weight of person on the new planet is,

W' = mg'

Here, g' is the gravitational acceleration on the new planet.

Let us calculate the gravitational acceleration on the new planet. The standard expression for the gravitational acceleration on the new planet is,

$g'=\dfrac{GM}{R^{2}}$

Here,

G is the universal gravitational constant.

M is the mass of planet, which is two times the mass of Earth. (M = 2m )

R is the radius of planet, which is twice the radius of Earth. (R = 2r).

Then,

$g'=\dfrac{G \times (2m)}{(2r)^{2}}\\\\g'=\dfrac{2(G \times m)}{4r^{2}}\\\\g'=\dfrac{1}{2} \times \dfrac{(G \times m)}{r^{2}}\\\\g'=\dfrac{1}{2} \times g$

Here, g is the gravitational acceleration value on Earth. And its value on Earth is $9.8 \;\rm m/s^{2}$ .

Then,

$g'=\dfrac{g}{2} \\\\g'=\dfrac{9.8}{2}\\\\g'=4.9 \;\rm m/s^{2}$ .

Calculate the mass as,

$W =mg\\500 = m \times 9.8\\m \approx 51 \;\rm kg$

So weight of person on new planet will be,

$W' = 51 \times 4.9\\W' \approx 250 \;\rm N$

Thus, we can conclude that the weight of person on the new planet is of 250 N.

Learn more about the gravitational acceleration here:

link

Answer from: Quest

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Answer from: Quest

Pe = 1/2k(x)^2 and .05n/m = .05x10^-9m = x

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Anew planet is discovered that has twice the earth's mass and twice the earth's radius. on the surfa...

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