Final distance from the centre of earth wil be $R+9R=10R$.

Now acceleration due to gravity at any height(distance from centre r) is given by,

$g=\frac{GM}{r^2}$.

Therefore,

$g^{\text{'}}=\frac{GM}{{\left(10R\right)}^2}$

Now, value of $g$ at surface will be, $\frac{GM}{R^2}$.

Hence,

$g^{\text{'}}=\left(\frac{g}{100}\right)$.

Then, $W^{\text{'}}=m{g}^{\text{'}}=\frac{mg}{100}=\frac{W}{100}$