Question

a smooth inclined plane is fixed in a car accelerating at
$a = g \tan( \alpha )$
If the sphere is set pure rolling on the incline then

a) it will continue rolling
b) it will slip down
c)its linear velocity will increase
d) its linear velocity will decrease.​

Answer 1

The freebody diagram of the setup will be as given above.

Here ma acts as pseudo force as the incline is at rest wrt car.

Now,

$f \: net = macos \alpha - mgsin \alpha$

Substituting a=g tan(alpha)

both the terms cancel out.

We get, Fnet=0