First slide

Pseudo force

Question

A block of mass m is placed on a smooth inclined wedge A B C 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

Moderate

A

$a = \frac{g}{cosec θ}$
B

$a = \frac{g}{\sin θ}$
C

$a = g \cos θ$
D

$a = g \tan θ$

Solution

In non-inertial frame,
$N \sin θ = m a . . . . . . . . (i)$
$N \cos θ = m g . . . . . . . . . (i i)$
From (i) and (ii),
$\begin{array}{l} \tan θ = \frac{a}{g} \\ a = g \tan θ \end{array}$

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