Use differentials to estimate the change in tension of yo-yo string

[bubbers]

. Homework Statement

The tension T in the string of the yo-yo is given by:

T=(mgR)/(2r^2+R^2)

where m is the mass of the yo-yo and g is the acceleration due to gravity. Use differentials to estimate the change in tension if R is increased from 3cm to 3.1cm and r is increased from 0.7cm to 0.8cm. Does the tension increase or decrease?

Homework Equations

I assume you'd need

dT=∂T/∂r*dr + ∂T/∂R*dR

The Attempt at a Solution

I'm not completely sure how to approach this problem. My guess is that you need to find the partials, and then use the values to which r and R increase somehow, maybe as dr and dR values...but I'm not sure how to go about that.
Any help would be greatly appreciated :)

 

[Mark44]

. Homework Statement

The tension T in the string of the yo-yo is given by:

T=(mgR)/(2r^2+R^2)

where m is the mass of the yo-yo and g is the acceleration due to gravity. Use differentials to estimate the change in tension if R is increased from 3cm to 3.1cm and r is increased from 0.7cm to 0.8cm. Does the tension increase or decrease?

Homework Equations

I assume you'd need

dT=∂T/∂r*dr + ∂T/∂R*dR

The Attempt at a Solution

I'm not completely sure how to approach this problem. My guess is that you need to find the partials, and then use the values to which r and R increase somehow, maybe as dr and dR values...but I'm not sure how to go about that.
Any help would be greatly appreciated :)

This is a good start. In place of dr and dR, approximate them with Δr = .1 (cm) and ΔR = .1 (cm). Evaluate your two partials using r = .7 cm and R = 3 cm.