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Work-Energy Theorem

A block of ma...

Question

A block of mass m is placed on a wedge. The wedge can accelerate in four manners marked as (1), (2), (3) and (4) as shown in the figure. If the normal reactions in situations (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 and if $a < \frac{3 g}{4},$ then

A

N_{3} > N_{1} > N_{2} > N_{4}

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B

b_{2} > b_{3} > b_{4} > b_{1}

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C

b_{2} > b_{3} > b_{1} > b_{4}

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D

N_{4} > N_{3} > N_{1} > N_{2}

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Solution

The correct options are
A $N_{3} > N_{1} > N_{2} > N_{4}$
B $b_{2} > b_{3} > b_{4} > b_{1}$

$N_{1} = m g c o s 37^{\circ} + m a s i n 37^{\circ} N_{2} = m g c o s 37^{\circ} - m a s i n 37^{\circ} N_{3} = m g c o s 37^{\circ} + m a c o s 37^{\circ} N_{4} = m g c o s 37^{\circ} - m a c o s 37^{\circ} N_{3} > N_{1} > N_{2} > N_{4} b_{1} = g s i n 37^{\circ} - a c o s 37^{\circ} b_{2} = g s i n 37^{\circ} + a c o s 37^{\circ} b_{3} = g s i n 37^{\circ} + a s i n 37^{\circ} b_{4} = g s i n 37^{\circ} - a s i n 37^{\circ} b_{2} > b_{3} > b_{4} > b_{1}$

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