A block of mass m is placed on a wedge The wedge can be accelerated in four manners marked as `(1),(2),(3)` and (4) as shown. If the normal reactions in situation `(1),(2),(3)` and (4) are `N_(1),N_(2),N_(3)` and `N_(4)` respectively and acceleration with which the block slides on the wedge in situation are `b_(1),b_(2),b_(3)` and `b_(4)` respectively then

Options

A. `N_(3) gt N_(1) gt N_(2) gt N_(4)`
B. `N_(4) gt N_(3) gt N_(1) gt N_(2)`
C. `b_(2) gt b_(2) gt b_(4) gt b_(1)`
D. `b_(2) gt b_(2) gt b_(1) gt b_(4)`

Answer

A, C

Explanation

For case-1, Balancing forces perpendicular to incline
`N_(1) = mg cos 37^(@) + ma sin 37^(@)`
`N_(1) = (4)/(5) mg + (3)/(5) ma`
And along incline,
`mg sin 37^(@) - ma cos 37^(@) = m b_(1)`
`B_(1) = (3)/(5) g - (4)/(5) a`
similarly, for case-2 we get,
`N_(2) = (4)/(5) mg - (3)/(5) ma`
and `b_(2) = (3)/(5) g + (4)/(5) a`
similarly, for case - 3, we get
`N_(3) = (4)/(5) mg + (4)/(5) ma`
`b_(3) = (3)/(5) g + (3)/(5) a`
similarly, for case-4 we get
`N_(4) = (4)/(5) mg - (4)/(5) ma`
and `b_(4) = (3)/(5) g - (3)/(5) a`.