The maximum tension a rope can withstand is 60 kg.wt. The ratio of maximum acceleration with which two boys of masses 20 kg and 30 kg can climb up the rope at the same time is

Options

A. `1:2`
B. `2:1`
C. `4:3`
D. `3:2`

Answer

D

Explanation

`60 kg-wt = 20 (g + a_(1)) + 30 (g + a_(2))`
`60 kg-wt = 20 kg-wt + 20a_(1) + 30 kg-wt + 30 a_(2)`
`(because g = kg-wt)`
` therefore 20 a_(1) + 30 a_(2) = 10 kg-wt`
`2a_(1) + 3a_(2) = 1`
For this equation to be equal to 1 .
`2a_(1) =1/2 , 3a_(2) = ½`
`therefore a_(1)=1/4, a_(2)=1/6`
`a_(1):a_(2)= ¼:1/6= 6:4=3:2`