T_{1} = T_{2} = m^{2}_{1}/r + mg + = m/r (v^{2}_{1} + gr)

T_{2} = L_{H} = m/r(v^{2}_{1} - 2gh) + mg({r - h}/{r})

Since h = 2r

We have, T_{2} = m/r(v^{2}_{1} - 4gr) + mg({r - 2r}/{r})

= m/r(v^{2}_{1} - 4gr) - mg

Therefore, T_{1} - T_{2} = m/r(v^{2}_{1} + gr) - m/r(v^{2}_{1} + 4gr) + mg

= 6 mg