Rotational

2)A ball is whirled in a circle by attatching it to a fixed point with a string.Is there any angular rotation of the ball about its centre?If yes,is this angular velocity equal to the angular velocity of the ball about the fixed point?

Think of this closely. Try to do the same to a ball. I am sure you will get the answer to this one :)

3)The torque of the wieght of any body about any vertical axis is zero.Is it always correct?

Torque = rxF

when will rxF be zero? eiter r=0 or r and F parallel

Now do you have the answer?

4)The torque of a force F about a point is defined as Γ =r X F .Suppose r, F, Γ are all non-zero.Is r X Γ || F always true?.Is it ever true?

two things are parallel if their cross product is zero

(rxΓ)xF = what will it be?

Think just a bit.. you are very close to the answer

7) A rectangular brick is kept on a table with a part of its length projecting out.It remains at rest if the length projected is slightly less than half the total lenghth but it falls down if the lenght projected is slightly more than half the total lenght.Explain.

This is because of the torque about the edge of the table.

Try balancing torque there. The answer will be found :)

8) When a very fat person tries to touch his toes,keeping the legs straight,he generally falls.Explain.

Torque gets unbalanced.
Where is N acting. Where is Mg acting.
What will be the torque. We had done one problem of shifting of the point of normal reaction in the class arpan if you remember :)

9) When tall buildings are constructed on earth,the duration of day-night slightly increases.Is it true?

This has to do with moment of Inertia. First hint (Will I of the earth increase of decrease)
2nd Hint: Will angular momentum be conserved?

These yield the answer :)

10) If the ice at the poles melts and flows towards the equator ,how will it affect the duration of day and night?

The Moment of inertia will increase or decrease?

Refer to the hints in the Question 9

1)Can an object be in pure translation as well as in pure rotation?

This is a very tricky one.. can you think a bit more

Hint: take two points on the body.