It is important that an electric table lamp with a lamp shade does not get knocked over easily.
Which statement is correct?
Correct Answer: \( \boxed{\mathrm{A}} \)
An object is more stable when its centre of mass is lower and its weight acts well within its base.
A low centre of mass makes it more difficult for the line of action of the weight to move outside the base when the object is tilted.
This means a larger tilt is required before the lamp topples over.
A heavy shade would raise the centre of mass and make the lamp less stable.
A narrow base also reduces stability because the lamp can tip more easily.
Therefore, the most important requirement is that the centre of mass is as low as possible.
Hence, the correct answer is (A).
An irregular plane object is suspended freely from point \(O\). The object is displaced and then released. It swings a few times and comes to rest as shown.
Where is the centre of gravity of the object?
Correct Answer: \( \boxed{\mathrm{D}} \)
When an object is freely suspended, it rotates until it reaches a position of stable equilibrium.
The weight of the object acts vertically downward through its centre of gravity.
If the centre of gravity is not directly below the suspension point, the weight produces a turning moment that causes the object to rotate.
The object comes to rest only when there is no resultant moment about the suspension point.
At equilibrium, the line of action of the weight passes through the point of suspension \(O\).
Therefore, the centre of gravity must lie on the vertical line through \(O\) and be below it.
Hence, the centre of gravity is vertically below \(O\).
Therefore, the correct answer is (D).
A child has four blocks of wood in the shapes of the letters A, M, T and X.
The blocks have equal heights and thicknesses. At their widest parts, their widths are equal.
The child stands the four blocks the right way up on a flat table.
Which block is most likely to fall over when the block is slightly knocked?
Correct Answer: \( \boxed{\mathrm{C}} \)
The stability of an object depends on the position of its centre of gravity and the width of its base.
An object is less stable when it has a high centre of gravity and a narrow base of support.
The letter T has most of its mass concentrated near the top and is supported by a relatively narrow vertical stem.
When the block is slightly knocked, the line of action of its weight can easily move outside its base, causing it to topple.
The letters A, M and X have wider supporting regions and generally lower centres of gravity, making them more stable.
Therefore, the letter T is the most likely to fall over when slightly disturbed.
Hence, the correct answer is (C).
