Question

the masses of the system r taken such that m doesn't slide over M not (M0) . All the surfaces r frictionless​

Answer 1

Answer:

Method 1 : Analysis of forces on m relative to ground

IF the motion of m is analyzed from ground, its acceleration is A and the forces acting on it are its weight mg and normal reaction N. Asm is at rest, moving with same acceleration as wedge in horizontal direction but in vertical direction, the block is at rest.

∑

F

y

=0⇒Ncosθ=mg........(i)

∑

F

x

=∑m

i

a

i

⇒Nsinθ=mA.........(ii)

On solving (i) and (ii), we get A=g

tanθ and N=

cosθ

mg

Method 2 : Analysis of forces on m relative to the inclined plane

If the motion of m is analyzed from the view point of an observer standing on the inclined plane (i.e., relative to the plane), its acceleration is 0 and the forces acting on it are : its weight. the normal reaction and a pseudo force of magnitude mA towards left.

mAsinθ=mAcosθ

⇒ A=gtanθ

Also: N=mgcosθ+mAsinθ

mgcosθ+mgtanθsinθ=

cosθ

mg