Question

An object weighs 10N on earth .what is the objects weight on a planet one tenth the earths mass and one half its radius?

Answer 1

We know, weight = mass * gravity 
10 = m * 9.8
m = 10/9.8 = 1.02 Kg

Now, Let, the gravity of that planet = g'
g' = m/r²   [m,r = mass & radius of that planet ]
g' = M/10 / (1/2R)²   [M, R = mass & radius of Earth ]
g' = 4M / 10R²
g' = 2/5 * M/R²
g' = 2/5 * g   
g' = 2/5 * 9.8
g' = 3.92

Weight on that planet = planet's gravity * mass
W' = 3.92 * 1.02
W' = 4 N

In short, Your Answer would be 4 Newtons

Hope this helps!