Question

a body has a weight W on the surface of the earth. What is the weight on a planet whose mass is 15 times that of earth and a radius that is 4 time that of the earth

Answer 1

g = GM/r^2

G - gravitational constant
M - mass of body
r - radios

From the above equation, it is clear that the acceleration due to gravity is directly proportional to the mass and inversely proportional to the square of the radius of the object. It mean if u increase mass 15 time then g will also increase by 15 times. and if u increase radios by 4 time then g will decrease by 16 times.

so new acc due to gravity will be 15/16 of the old one.
New g = 15/16 × 9.8 = 9.18 m/s^2 {g of earth=9.8}

Now to find new weight , just multiply the mass ( weight / 9.8) with 9.18 (new g)

Answer 2

The weight of a body on the surface of earth= W nrwton.means that W=mg, where m is the mass if the body and g is gravity of earth surface.now we have to find the weight of the same body at other planet whose mass is 15 times of earth and radius is 4 times of the earth. Let the weight OK f the body at new planet is W1, means W1= mg1, where m us the mass if the body and g1 is the gravity of the planet.now g1= G.15M/(4R)^2 ,M=mass of earth & R= radius if earth.so g1= 15/16g.now W1 = mg1= m.15/16g= 15/16W newton.