TEST YOURSELF

Two forces each of magnitude $2 \mathrm{N}$ act vertically upwards and downwards respectively on the two ends of a uniform rod of length $1 \mathrm{m}$ freely pivoted at its centre. Determine the resultant moment of the force about the mid-point of the rod.

A uniform metre scale balances horizontally on a knife-edge placed at $55 \mathrm{cm}$ mark when a mass of $25 \mathrm{g}$ is suspended from one end. Draw a diagram of this arrangement. Calculate the mass of the scale.

From the given figure, calculate moment of force about (i) $\mathrm{P}$, and (ii) $\mathrm{Q}$.

The iron gate of a building is $3 \mathrm{m}$ broad. It can be opened by applying $100 \mathrm{N}$ force at the middle of the gate. Calculate the least force required to open this gate. Where should the force be applied?

In the given diagram wheel shown has a fixed axle passing through $O$. The wheel is kept stationary under the action of two force $F_1$ and $F_2$ such that (i) a horizontal force $F_1$ at $P$ (ii) a vertical force $F_2$ at $Q$. Show the direction of $F_2$ in the diagram. Which is the greater force? Find the ratio between the forces.
(Given : $PO=2.5 \mathrm{cm}$, $QO\text{'}=1.5 \mathrm{cm}$ and $OO\text{'}=2.0 \mathrm{cm}$)

A square cardboard is suspended by passing a pin through a narrow hole at its one corner. Draw a diagram to show its rest position. In the diagram, mark the point of suspension by letter $\mathrm{S}$ and centre of gravity by letter $\mathrm{G}$.

The position of centre of gravity of a body remains unchanged even when the body is deformed.

A ball is hanging by a thread from the ceiling of the roof. Draw a neat labelled diagram showing the forces acting on the ball and the string.