A block of mass m is placed on a smooth 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

Question

A block of mass m is placed on a smooth 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 down relative to the wedge in situations are $b_{1}, b_{2}, b_{3}$ and $b_{4}$ respectively then: [Take $a < g$ ]

TestHub · Accepted Answer

(1) (2) (3) (4) All FBD are in non-inertial reference frame

$N_{1} = mg cos θ + ma sin θ$

$mg sin θ - ma cos θ = mb_{1}$

$N_{2} = mg cos θ - ma sin θ$

$mg sin θ + ma cos θ = mb_{2}$

$N_{3} = (ma + mg) cos θ$

$(ma + mg) sin θ = mb_{3}$

$N_{4} = mg cos θ - ma cos θ$

$mg sin θ - ma cos θ = mb_{4}$

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