A block of mass is placed on a smooth inclined wedge ABC of inclination as shown in the figure. The wedge is given an acceleration towards the right. The relation between and for the block to remain stationary on the wedge is [2018]

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Solution

Q.
A block of mass $m$ is placed on a smooth inclined wedge ABC of inclination $θ$ as shown in the figure. The wedge is given an acceleration $a$ towards the right. The relation between $a$ and $θ$ for the block to remain stationary on the wedge is [2018]

1 $a = \frac{g}{c o s e c θ}$

2 $a = \frac{g}{\sin θ}$

3 $a = g \cos θ$

4 $a = g \tan θ$

Ans.
(4)

In non-inertial frame,

$N \sin θ = m a$ ...(i)

$N \cos θ = m g$ ...(ii)

From (i) and (ii),

$\tan θ = \frac{a}{g}$

$\Rightarrow a = g \tan θ$

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