A uniform metre rule has masses 20g and 10g hung at the 10cm mark and at the 30cm mark respectively . Calculate the value of m required to balance the rule horizontally
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To balance the uniform meter rule horizontally, the torques on either side of the fulcrum must be equal.
The torque is calculated by multiplying the force by the distance from the fulcrum. In this case, the force is the weight of each mass (m*g), and the distances are 10 cm on one side and 70 cm on the other side (100 cm total length - 30 cm mark).
On the side of the 20g mass (10cm mark):
Torque1 = (m1 * g) * d1
On the side of the 10g mass (30cm mark):
Torque2 = (m2 * g) * d2
Since the rule is balanced horizontally, the torques are equal:
Torque1 = Torque2
Substituting the given values:
(m1 * g) * d1 = (m2 * g) * d2
m1 = 20g = 0.02 kg
m2 = 10g = 0.01 kg
d1 = 10 cm = 0.10 m
d2 = 70 cm = 0.70 m
Thus, the equation becomes:
(0.02 kg * g) * 0.10 m = (0.01 kg * g) * 0.70 m
Simplifying the equation:
0.002 kg * g = 0.007 kg * g
The "g" term cancels out on both sides, leaving:
0.002 kg = 0.007 kg
To solve for "m" in the equation, we divide both sides by 0.002 kg:
0.007 kg / 0.002 kg = m
Therefore, the value of "m" required to balance the rule horizontally is:
m = 3.5
To balance the uniform meter rule horizontally, the torques on each side of the rule need to be equal. The torque on each side is obtained by multiplying the mass hanging at a certain distance by that distance.
Let's call the unknown mass m.
On the left side of the rule (10 cm side), the torque is given by:
Torque_left = mass_left * distance_left
The known values on the left side are:
mass_left = 20g
distance_left = 10 cm = 0.1 m
So, Torque_left = 20g * 0.1m
On the right side of the rule (30 cm side), the torque is given by:
Torque_right = mass_right * distance_right
The known values on the right side are:
mass_right = 10g
distance_right = 30 cm = 0.3 m
So, Torque_right = 10g * 0.3m
For the rule to balance horizontally, the torques on both sides must be equal.
Therefore, we can set up the equation:
Torque_left = Torque_right
20g * 0.1m = 10g * 0.3m
To simplify the equation, we can convert the masses from grams to kilograms by dividing by 1000:
(20g / 1000) * 0.1m = (10g / 1000) * 0.3m
0.02 * 0.1m = 0.01 * 0.3m
0.002m = 0.003m
To solve for m, we can divide both sides of the equation by 0.003:
m = 0.002m / 0.003
m ≈ 0.6667 kg
Therefore, the value of m required to balance the rule horizontally is approximately 0.6667 kg.