Question

250 N force is required to raise 75 kg mass from a pulley. If rope is pulled 12 m then the load is lifted to 3m, the efficiency of pulley system will be : -

• A. 0.25
• B. 0.333
• C. 0.75
• D. 0.9

Answer 1

The Correct Option is C

To find the efficiency of the pulley system, we need to understand the relation between work input, work output, and efficiency. The efficiency of a system can be calculated using the formula:

Efficiency (\eta) = \frac{\text{Work Output}}{\text{Work Input}} \times 100\%

1. Calculate the work input:
   • The force applied to pull the rope is \(250 \, \text{N}\), and the distance the rope is pulled is \(12 \, \text{m}\).
   • Work input = Force x Distance = \(250 \, \text{N} \times 12 \, \text{m} = 3000 \, \text{J}\).
2. Calculate the work output:
   • The work done in lifting the mass is given by the formula: Work output = Weight x Height lifted.
   • Weight of the mass = \(75 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 735 \, \text{N}\).
   • Height to which the mass is lifted = \(3 \, \text{m}\).
   • Work output = \(735 \, \text{N} \times 3 \, \text{m} = 2205 \, \text{J}\).
3. Calculate the efficiency:
   • Efficiency = \(\frac{2205 \, \text{J}}{3000 \, \text{J}} \times 100\%\).
   • Efficiency = \(0.735 \times 100\% = 73.5\%\).
   • Rounding this to two decimal places, it is \(0.75\), which matches one of the given options.

Therefore, the efficiency of the pulley system is 0.75 or 75%.