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

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

Aicharya · Accepted Answer

In non-inertial frame of wedge
Using pseudo force,
Free body diagram is given as

Normal reaction is balanced by $m g \cos (θ)$

Where m is mass of the body,

g is the acceleration due to gravity

a is the acceleration produced by external force..
$m a \cos θ = m g \sin θ$

$a = \frac{g \sin (θ)}{\cos (θ)}$
$a = g \tan θ$

A block of mass m is placed on a smooth inclined wedge A B C of inclination θ as shown in the figure. The…