$2$ Fig. $2\mathrm{.}1$ shows a spring balance used to measure the weight of a baby. The spring inside the

balance extends when a mass is suspended from it$.$ The dial shows the extension of spring as a

value of mass in kg $.$

Fig. $2\mathrm{.}1$

The spring obeys Hooke's law up to a weight of $175$ N $.$

a$)$ The reading on the spring balance is $8\mathrm{.}0$kg$.$ Determine the force exerted on the spring due to the baby.

b$)$ The baby is carried from the ground floor to the bedroom. The vertical height of the bedroom above the ground floor is $3\mathrm{.}5$m$.$ Calculate the change in gravitational potential energy of the baby when it is carried from the ground floor to the bedroom.