A uniform pencil AB weiging 40g can be balanced holizontally on a knife edge at 2cm at the end where a mass of 60g is hung from the end, what is the length of the pencil?
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To find the length of the pencil, we can use the principle of moments. The principle of moments states that for an object in equilibrium, the sum of the clockwise moments is equal to the sum of the anticlockwise moments.
In this case, we have a pencil AB that is balanced on a knife edge at a distance of 2 cm from one end. A mass of 60 grams is hanging from the other end. Let's denote the length of the pencil as L.
To balance the pencil, the clockwise moment due to the hanging mass (60 grams) at a distance (L) must be equal to the anticlockwise moment due to the weight of the pencil (40 grams) at a distance (2 cm).
Clockwise Moment = Mass x Distance
Anticlockwise Moment = Mass x Distance
Clockwise Moment = 60 grams x L (since the mass is hanging at a distance L from the knife edge)
Anticlockwise Moment = 40 grams x 2 cm
Setting the clockwise moment equal to the anticlockwise moment:
60 grams x L = 40 grams x 2 cm
Now we can solve for L:
60L = 80
Dividing both sides of the equation by 60:
L = 80/60
Simplifying the fraction:
L = 4/3 cm
So, the length of the pencil (AB) is 4/3 cm.