91Ó°ÊÓ

Apply the following relation.

\(W = mg\)

Here, W is the weight of the child and basket, m is the mass of the child and basket, and g is the acceleration due to gravity.

Substitute 55N for W and 9.8 m/s² for g in the above expression, and we get,

\(\begin{array}{c}55\;{\rm{N}} = m \times 9.8\;{\rm{m/}}{{\rm{s}}^{\rm{2}}}\\m = \frac{{55\;{\rm{N}}}}{{9.8\;{\rm{m/}}{{\rm{s}}^{\rm{2}}}}}\\m = 5.6\;{\rm{kg}}\end{array}\)

Hence, the mass of the child and basket is 5.6 kg.

Referring to the figure, the tension T₁ will be equal to the weight of the child and basket.

Therefore, T₁=55 N.

Referring to the figure, the tension T2 will be equal to the weight of the weighing scale along with the weight of the child and basket.

\({T_2} = W + {m_w}g\)

Here, T2 is the tension in the cord connecting the weighing scale and the ceiling, and m₁ is the mass of the weighing scale.

Substitute 55 N for W, 0.5 kg for m₁, and 9.8m/s² for g.

\(\begin{array}{c}{T_2} = 55\;{\rm{N}} + 0.5\;{\rm{kg}} \times 9.8\;{\rm{m/}}{{\rm{s}}^{\rm{2}}}\\ = 55\;{\rm{N}} + 4.9\;{\rm{kg}} \cdot {\rm{m/}}{{\rm{s}}^{\rm{2}}}\\ = \left( {55 + 4.9} \right)\;{\rm{N}}\\ = 59.9\;{\rm{N}}\end{array}\)

Hence, the tension T2 in the cord is 59.9 N.