In a machining operation, doubling the cutting speed reduces

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In a machining operation, doubling the cutting speed reduces the tool life to 1/8th of the original value. The exponent n in Taylor's tool life equation VTⁿ = C. is

1. 1
  8
2. 1
  4
3. 1
  3
4. 1
  2

Correct Option: C

Taylor’s tool life equation,
VTⁿ = C ...(i)
Where, V = cutting speed and T = tool life
When cutting speed is doubled and tool life reduces to 1/8, then

2V		1	T		ⁿ	= C ...(ii)
		8

Dividing equation (i) by equation (ii), we get

VTⁿ			= 1
2V
	T	ⁿ
	8

or VTⁿ = 2V		T		ⁿ	= 2Vⁿ2⁻³ⁿ
		8

or 1 = 2⋅2⁻³ⁿ
or 1 = 2^{−3n + 1}
or 2^{−3n + 1} = 2⁰
or –3n + 1 = 0
or 3n = 1

or n =	1	.
	3