A uniform pencil AB of mass 4.0g can be balanced horizontally about a knife edge at 2cm from the end A when a mass of 6.0g is hang from this end. What is the length of the pencil.
To find the length of the pencil, we can start by setting up the equation of moments.
The equation of moments states that the moments on either side of a pivot point must balance each other out.
In this case, the pivot point is at the knife edge, and we have two moments to consider: the moment due to the pencil's weight and the moment due to the hanging mass.
Let's label the length of the pencil as "x" and the distance of the knife edge from end A as "d" (which is given as 2cm, or 0.02m).
The moment due to the pencil's weight is given by the formula: Moment = mass x distance x 9.8 (where 9.8 is the acceleration due to gravity).
The moment due to the hanging mass is given by the formula: Moment = mass x distance x 9.8.
Since the pencil is in equilibrium (balanced), the two moments must be equal.
The moment due to the pencil's weight can be calculated as: (4.0g/1000) x (x - d) x 9.8 (Note: we divide by 1000 to convert grams to kilograms).
The moment due to the hanging mass is: (6.0g/1000) x d x 9.8.
Setting these two moments equal to each other and solving for x, we get:
(4.0g/1000) x (x - 0.02) x 9.8 = (6.0g/1000) x 0.02 x 9.8.
Simplifying the equation:
0.0392(x - 0.02) = 0.0196
0.0392x - 0.000784 = 0.0196
0.0392x = 0.020384
x = 0.520cm
Therefore, the length of the pencil is 0.520cm.