a block of mass m is placed on a smooth wedge of inclination theta.the whole system is acclerated horizontally so that the block has a magnitude equal to???

Question

a block of mass m is placed on a smooth wedge of inclination
theta the whole system is acclerated horizontally so that the block
has a magnitude equal to???

Himanshu · Accepted Answer

Let the wedge be accelerated horizontally with an acceleration a

$A l o n g t h e i n c l i n e d p l a n e : m a \cos θ = m g \sin θ \Rightarrow a = g \tan θ N = m g \cos θ + m a \sin θ N = m g \cos θ + m (g \tan θ) \sin θ N = m g \cos + m g \frac{\sin^{2} θ}{\cos θ} = m g (\frac{\cos^{2} θ + \sin^{2} θ}{\cos θ}) = \frac{m g}{\cos θ}$