Question

a uniform cubical slab of side a is released from rest in the position as shown in the figure for what value of x is the angular acceleration maximum provided that the friction between surface and the cube is sufficient to prevent any slipping

Answer 1

At horizontal position the reaction 'N'.

Let the mass of rod is m.

The moment of inertia of rod about the axis passig through the end and perpendicular to its plane is

I=

3

1

ml

2

For rotation of rod,

Moment of force = Applied torque

⟹x×F=Iα

⟹α=

3

1

ml

2

xF

=

ml

2

3xF

Here α is angular acceleration about hinge .

The position of centre of mass is aat the middle.

So the linear acceleration of centre of mass,a=α

2

l

a=

2ml

3xF

So, the net force in vertical on centre of mass is

=ma

=

2l

3xF

This should be equal to N.

So, N=

2l

3xF