Rotation

1.A square is made by joining four rods each of mass M and length L.Its moment of inertia about an axis,in its plane and passing through one of its corner is
(a)6ML² (b)4ML²3 (c)8ML²3 (d)10ML²3

2.A thin rod of length 4l,mass 4m is bent at the points to make a shape of w with each corner perpendicular to each other.What is the moment of inertia of the rod passing through the middle point,i.e,through the junction of the 2nd and 3rd rod,perpendicular to the plane of the paper
(a)ml²3 (b)10ml²3 (c)ml²12 (d)ml²24

3.Linear mass density of the two rods system,AC and CB is x.Moment of inertia about an axis passing through AB is(angle ACB=90° ABC is an isosceles triangle)
(a)xl³4√3 (b)xl³√2 (c)xl³4 (d)xl³6√2

4.Assertion:A small ball is released from rest from the rim of a hemispherical bowl.If bowl is smooth then ball will exert more pressure at the lowest position,compared to the situation when bowl is rough.
Reason:Linear velocity and hence,centripetal force in smooth situation is more.

5.Assertion:A horizontal force F is applied at the centre of solid sphere placed over a plank.The minimum coefficient of friction between plank and sphere required for pure rolling is x,when plank is kept at rest and y when plank can move,then x>y.
Reason:Work done by frictional force on the sphere in both cases is zero.

6.From a uniform square plate of side a and mass m,a square portion DEFG of side a2 is removed.Then,the moment of inertia of remaining portion about the axis AB is
(a)7ma²16 (b)3ma²16 (c)3 ma²4 (d)9ma²16