Question

The mass of a body is 50 kg on the surface of the earth. find its weight on the surface of a planet whose mass is doubled than the mass of the earth and its radius is five times the radius of the earth.

Answer 1

Answer:

40N

Step by step explanation:

It is given that:

• The mass of the body on Earth = 50 kg.
• Mass on the planet = 2*Mass on Earth = 100 kg.
• Radius of the planet is 5 times the radius of the Earth

We need to find the weight of the body on that planet.

First of all, we need to calculate the gravitational force of acceleration 'g' of that planet. 'g' is directly proportional to the mass, and inversely proportional to the square of the radius.

Therefore,

$\frac{g_e}{g_2}=\frac{\frac{m_e}{r_e^2} }{\frac{m_2}{r_2^2} }\\ \\\frac{10}{g_2}=\frac{m_er_2^2}{m_2r_e^2}\\\\\frac{10}{g_2}= \frac{m_e(5r_e)^2}{2m_e(r_e^2)}\\\\\frac{10}{g}= \frac{25}{2}\\ g=0.8\:m/s^2$

Weight = m*g = 50*0.8 = 40 N

Answer 2

g' = GM' / R'^2

g' = G(2M) / (4R)^2

g' = GM / 8R^2

g' = g / 8

g' = 9.8 / 8

g' = 1.225 m/s^2

Weight of the body on planet is -

W = mg'

W = 40 × 1.225

W = 49 N