A uniform AB weighing 40g can be balanced horizontally on a knife edge at 2 cm from the end A when mass of 60 is hung from this end what is the length of a pencil
Asking
Well, I suppose the length of a pencil is usually around 15 centimeters, but I must say I'm not quite sure how that relates to balancing a uniform AB weighing 40g on a knife edge. Maybe the pencil can join in on the balancing act and provide some comic relief?
To determine the length of the pencil, we need to use the principle of moments. The principle of moments states that the sum of the clockwise moments about a point is equal to the sum of the anticlockwise moments about the same point.
In this case, we will consider the knife edge as the point of balance. Let's assume the length of the pencil is "x." We can set up the equation as follows:
Clockwise moment = anticlockwise moment
(clockwise moment due to the weight of the pencil) = (anticlockwise moment due to the weight hanging at end A)
40g (distance from A to the knife edge) = 60g (distance from the knife edge to the hanging weight)
40 * 2 = 60 * x
80 = 60x
Divide both sides by 60:
x = 80/60
x = 4/3
Therefore, the length of the pencil is 4/3 or approximately 1.33 cm.
To find the length of the pencil, we can make use of the principle of moments.
The principle of moments states that for an object to be in equilibrium, the sum of the clockwise moments about any point is equal to the sum of the anticlockwise moments about the same point. In this case, we need to consider the balancing point of the uniform object on the knife edge.
Let's assume the length of the uniform object AB is "x" cm, and the distance from the balancing point (knife edge) to end B is also "x" cm. Therefore, the distance from the balancing point to end A is (2 cm + x cm).
Now, let's consider the clockwise moments and the anticlockwise moments acting about the balancing point:
Clockwise moments:
Due to the mass of 60g hung from end A, the clockwise moment is given by: 60g * (2 cm + x cm)
Anticlockwise moments:
Due to the uniform object AB weighing 40g, the anticlockwise moment is given by: 40g * x cm
Since the object is balanced, the clockwise moments and anticlockwise moments are equal. Thus, we can set up the following equation:
60g * (2 cm + x cm) = 40g * x cm
Simplifying the equation, we have:
120 g * cm + 60 g * x cm = 40 g * x cm
80 g * x cm = 120 g * cm
x = 1.5 cm
Therefore, the length of the pencil is 1.5 cm.