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Consider a balance scales comprising of beam with unequal length of arms where the fulcrum is very close to one end of the beam. (Such scales are called steelyard. For instance, it is often used to weigh a catch in fisheries.) The load is hanged on the shorter arm, while the balance about the fulcrum is obtained by sliding the counterweight along the longer arm. (See the picture.) Suppose the distance of the load hanging point from the fulcrum is fixed at \( 5\,\mathrm{cm} \). If the weight of the load is \( 80\,\mathrm{N} \), the balance is achieved as the counterweight is moved to the very end of the longer arm. If the weight of the load is \( 60\,\mathrm{N} \), the balance is achieved when the counterweight is moved to the distance of \( 30\,\mathrm{cm} \) from the fulcrum. What is the length of the beam? \[ \] Hint: The steelyard is based on the law of the lever. For balanced lever is: \( F_1\cdot a=F_2\cdot b \), where \( F_1 \) is the weight of the load in the distance \( a \) from the fulcrum and \( F_2 \) is the weight of the counterweight in the distance \( b \) from the fulcrum.