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Q.

A small block of mass m rests on a smooth wedge of angle $θ$ . With what horizontal acceleration ‘a’ should the wedge be pulled, as shown in Fig., so that the block falls freely?

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a

$g \sin θ$

b

$g \tan θ$

c

$g \cos θ$

d

$g \cot θ$

answer is C.

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Detailed Solution

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$\begin{array}{l} m g \cos θ = m a \sin θ \\ a = g \cot θ \end{array}$

When it will loose the contact it becomes a freely falling body i.e., normal reaction will be zero.

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A small block of mass m rests on a smooth wedge of angle θ . With what horizontal acceleration ‘a’ should the wedge be pulled, as shown in Fig., so that the block falls freely?