1.

Find the ratio of efforts required to raise a given load, when the angle of inclination of a given plank is changed from `60^(@)` to `30^(@)`. Also find the percentage change in the mechanical advantage.

Answer» The ratio of efforts `((E_(1))/(E_(2)))` is
`(E_(1))/(E_(2))=(mg sin theta_(1))/(mg sin theta_(2)) rArr (E_(1))/(E_(2))=(sin theta_(1))/(sin theta_(2))`
Substituting ` sin 60^(@)=(sqrt(3))/(2)` and ` sin 30^(@)=1//2`,
we get
`(E_(1))/(E_(2))=(sqrt(3))/(2)xx2=sqrt(3)`
`:. E_(1):E_(2)= sqrt(3):1`
Change in M.A. ` = (1)/(sin 30^(@))-(1)/(sin 60^(@))=2-(2)/(sqrt(3))`
`=2(1-(1)/(sqrt(3)))=2((sqrt(3)-1)/(sqrt(3)))`
% Change in MA = `("Change in MA")/("initial MA")xx100`
`=(2 (sqrt(3)-1))/(sqrt(3)xx(2)/(3))xx100=(sqrt(3)-1)xx100`
`= 0.732xx100=73.2%`


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