2A flat belt run over a pulley and transmitting the power of 2.5 KW. The linear velocity of the belt is 2.5 m/s. The angle of lap is 165° and the coefficient of friction between the belt and pulley is 0.3. If the initial tension of the belt is increased by 10%, what is the effect on power transmission? (neglecting the slip and centrifugal effect of the belt) 

Correct option is A

​$$\begin{aligned}&\textbf{1. Initial Power:} \\&P = (T_1 - T_2) \cdot v \\&\text{Given } P = 2.5\, \text{kW}, \quad v = 2.5\, \text{m/s} \Rightarrow T_1 - T_2 = \frac{2500}{2.5} = 1000\, \text{N} \\[1em]&\textbf{2. Tension Ratio (Capstan Equation):} \\&\frac{T_1}{T_2} = e^{\mu \theta} = e^{0.3 \times 2.88} \approx 2.37 \\&\text{Solve: } T_1 = 1730\, \text{N}, \quad T_2 = 730\, \text{N} \\[1em]&\textbf{3. Initial Tension } (T_0): \\&T_0 = \frac{T_1 + T_2}{2} = \frac{1730 + 730}{2} = 1230\, \text{N} \\[1em]&\textbf{4. After 10\% Increase in } T_0: \\&T_0' = 1.1 \times 1230 = 1353\, \text{N} \\&\text{New tensions: } T_1' = 1903\, \text{N}, \quad T_2' = 803\, \text{N} \\[1em]&\textbf{5. New Power:} \\&P' = (1903 - 803) \times 2.5 = 2750\, \text{W} = 2.75\, \text{kW} \\[1em]&\textbf{Result:} \\&\text{A } \mathbf{10\%} \text{ increase in initial tension increases power transmission by } \mathbf{10\%} \text{ (from 2.5 kW to 2.75 kW).}\end{aligned}$$​​