Questions in rotational-motion

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For a system to be in equilibrium, the torques acting on it must balance. This is true only if the torques are taken about
What is the torque of the force $\overset{\to }{\mathop{F}}\,=(2\hat{i}-3\hat{j}+4\hat{k})N$ acting at the pt. $\overset{\to }{\mathop{r}}\,=(3\hat{i}+2\hat{j}+3\hat{k})\,m$ about the origin
Two men are carrying a uniform bar of length $L$, on their shoulders. The bar is held horizontally such that younger man gets $(1/4)\,th$ load. Suppose the younger man is at the end of the bar, what is the distance of the other man from the end
A uniform meter scale balances at the $40\,cm$ mark when weights of $10\,g$ and $20\,g$ are suspended from the $10\,cm$ and $20\,cm$ marks. The weight of the metre scale is
A cubical block of side L rests on a rough horizontal surface with coefficient of friction $\mu $. A horizontal force F is applied on the block as shown. If the coefficient of friction is sufficiently high so that the block does not slide before toppling, the minimum force required to topple the block is
When a force of 6.0 N is exerted at ${{30}^{o}}$ to a wrench at a distance of 8 cm from the nut, it is just able to loosen the nut. What force F would be sufficient to loosen it, if it acts perpendicularly to the wrench at 16 cm from the nut
A person supports a book between his finger and thumb as shown (the point of grip is assumed to be at the corner of the book). If the book has a weight of W then the person is producing a torque on the book of
Weights of $1g,\,2g.....,100g$ are suspended from the 1 cm, 2 cm, ...... 100 cm, marks respectively of a light metre scale. Where should it be supported for the system to be in equilibrium
A uniform cube of side a and mass m rests on a rough horizontal table. A horizontal force F is applied normal to one of the faces at a point that is directly above the centre of the face, at a height $\frac{3a}{4}$ above the base. The minimum value of F for which the cube begins to tilt about the edge is (assume that the cube does not slide)
A circular disc of radius R and thickness $\frac{R}{6}$ has moment of inertia I about an axis passing through its centre and perpendicular to its plane. It is melted and recasted into a solid sphere. The moment of inertia of the sphere about its diameter as axis of rotation is

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