1.

A dip circle shows an apparent dip of 60^(@) at a place Where the true dip is 45^(@). If the dip eirele is rotated through 90^(@) , what apparent dip will it show?

Answer»

`40^(@)`
`45^(@)`
`51^(@)`
`57^(@)`

Solution :`theta_(1) 60^(@), theta = 45^(@), alpha = 90^(@)`
For a DIP circle, `cot^(@)theta = cot^(@) theta_(1) + cot^(@)theta_(2)`
where, `theta_(1) and theta_(2)` are the apparent dips in two perpendicular POSITIONS.
`therefore cot^(2)45^(@)=cot^(@)60^(@) + cot^(2)theta_(2)`
`implies (1)^(2) = (1/sqrt3)^(2)+cot^(2) theta_(2) [therefore TAN 60^(@) = sqrt3]`
`implies cot^(2) theta_(2) =1-(1/sqrt2)^(2)=1-1/3=2/3`
`implies cottheta_(2) = sqrt(2/3)=sqrt(0.67)=0.816`
`theta_(2) ~~ 51^(@).`


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