Question

In a process, the number of cycles to failure decreases exponentially with an increase in load. At a load of 80 units, it takes 100 cycles for failure. When the load is halved, it takes 10000 cycles for failure. The load for which the failure will happen in 5000 cycles is

• A. 40.00
• B. 46.02
• C. 60.01
• D. 92.02

Answer 1

The correct option is B 46.02

Let N = No. of cycles; t = load; N = $C_1{e}^{-c_{2}t}$

100 = $C_1{e}^{-80c_2}$ ...(1)

10000 = $C_1{e}^{-40c_2}$ ...(2)

$\Rightarrow 40C_2=ln100$

$\Rightarrow C_2=0.1151$

$\Rightarrow 100=C_1{e}^{-80\times 0.1151}$

$\Rightarrow C_1={10}^6$

Now, 5000 = ${10}^6{e}^{-t\times 0.1151}$

$\Rightarrow t=46.02$