Question

Comprehension

In a machining experiment, tool life was found to vary with the cutting speed in the following manner:

Cutting speed (m/min)	Tool life (minutes)
60	81
90	36

1. 50%
2. 200%
3. 300%
4. 400%

Answer 1

Correct Answer - Option 3 : 300%

n = 0.5, V2 = V1/2

\(\begin{array}{l} V{T^n} = C \Rightarrow V{T^{0.5}} = C \Rightarrow V \propto \frac{1}{{\sqrt T }}\\ So,\frac{{{V_2}}}{{{V_1}}} = \sqrt {\frac{{{T_1}}}{{{T_2}}}} \Rightarrow \frac{1}{2} = \sqrt {\frac{{{T_1}}}{{{T_2}}}} \Rightarrow \frac{{{T_1}}}{{{T_2}}} = \frac{1}{4} \Rightarrow {T_2} = 4{T_1} \end{array}\)

% increases in tool life \(= \frac{{{T_2} - {T_1}}}{{{T_1}}} \times 100 = 300\%\)