Forces, Density and Pressure

The diagram shows a child X of mass $20\text{ kg}$ and a child Y of mass $15\text{ kg}$ seated on a uniform plank.

The plank has a mass of $7.0\text{ kg}$ and has a pivot at its midpoint. The plank is horizontal and in equilibrium.
Which statement about the weight of the plank is correct?

Options

A   The weight of the plank can be considered to be acting at its midpoint.
B   The weight of the plank is causing an anticlockwise moment.
C   The weight of the plank is causing a clockwise moment.
D   The weight of the plank equals the force on the plank from the pivot.

An object is fully submerged in a liquid.
A student determines the ratio

$$\frac{\text{weight of the object}}{\text{upthrust acting on the object}}$$

Which single change would double the value of this ratio?

Options

A   Use a different liquid that has twice the density and the same volume as the original liquid.
B   Use a different object that has half the volume and the same density as the original object.
C   Use a different object that has twice the density and the same volume as the original object.
D   Use a different object that has twice the volume and the same density as the original object.

A shop sign weighing $75\text{ N}$ hangs from a frame attached to a vertical wall.

The frame consists of a horizontal rod XY and a rod YZ that is at an angle of $30^\circ$ to the horizontal.
Rod XY is attached to the wall by a hinge at X and has length $0.50\text{ m}$. Assume that the weights of the rods are negligible.
What is the horizontal force exerted by the wall on rod XY?

Options

A   $0\text{ N}$
B   $43\text{ N}$
C   $130\text{ N}$
D   $150\text{ N}$

The diagram shows a uniform plank XY of length $4.0\text{ m}$ and weight $300\text{ N}$.

The plank rests on fixed supports at its ends X and Y.
A child of weight $600\text{ N}$ stands in different positions on the plank.
The support at end X exerts a force $F$ vertically upwards on the plank.
What is the magnitude of $F$ when the child stands at X and when the child stands at Y?

Options

Which row describes a pair of forces that forms a couple?

Options

A uniform cylinder of weight $25.0\text{ N}$ is suspended from a newton meter.

The cylinder is fully submerged in water, as shown.

The reading on the newton meter is $10.0\text{ N}$.

The water is replaced by a liquid with a density $10\%$ greater than the density of water. The cylinder remains fully submerged.

What is the new reading on the newton meter?

Options

A   $8.5\text{ N}$
B   $9.0\text{ N}$
C   $11.0\text{ N}$
D   $11.5\text{ N}$

A student balances a $30\text{ cm}$ ruler on a fulcrum set at the $15\text{ cm}$ mark. She then places a $50\text{ g}$ mass on the $23\text{ cm}$ mark and a $20\text{ g}$ mass on the $11\text{ cm}$ mark, as shown.

Which mass should she place on the $7\text{ cm}$ mark to restore the balance?

Options

A   $30\text{ g}$
B   $40\text{ g}$
C   $47\text{ g}$
D   $133\text{ g}$

A submarine is at a depth of $130\text{ m}$ below the surface of the sea.

The pressure on the submarine due to the sea water is $p$.

The submarine sinks to a depth of $260\text{ m}$ below the surface.

Assume that the density of sea water is constant.

What is the difference between the pressures on the submarine due to the sea water at the two depths?

Options

A   $0$
B   $0.5p$
C   $p$
D   $2p$

A wooden block is held stationary in a container of water using a string that is attached to both the wooden block and the bottom of the container.

The wooden block has mass $m$ and volume $V$. The water has density $\rho$. The acceleration of free fall is $g$.

What is the magnitude of the force acting on the block due to the tension in the string?

Options

A   $\rho gV$
B   $mg + \rho gV$
C   $mg$
D   $\rho gV - mg$

A square shop sign of uniform density has mass $2.4\text{ kg}$ and sides of length $0.86\text{ m}$.

The sign is supported by a hinge along its top edge.

There is friction in the hinge so that the sign hangs from it in equilibrium at an angle of $15^\circ$ to the vertical, as shown.

What is the moment about the hinge of the weight of the sign?

Options

A   $2.6\text{ N m}$
B   $4.0\text{ N m}$
C   $5.2\text{ N m}$
D   $9.8\text{ N m}$