A meter rule is placed horizontally at a fixed point, 1 mass are suspended at both right hand and left hand of the meter. from the center of the meter rule, a masses is hung 20.5cm are wild from the center ...., a mass of 0.1kg is hung at other side from the center of ruler distance 45cm. find the mass required to balanced the meter rule.
I need solution to that
Solve the solution
To find the mass required to balance the meter rule, we need to consider the torque being exerted on both sides of the ruler.
First, let's calculate the torque exerted by the 0.1 kg mass hanging at a distance of 45 cm from the center of the ruler.
Torque = force x distance
The force exerted by the 0.1 kg mass can be calculated using Newton's second law:
Force = mass x acceleration due to gravity
Given that the mass is 0.1 kg and the acceleration due to gravity is approximately 9.8 m/s^2:
Force = 0.1 kg x 9.8 m/s^2
Force = 0.98 N
Now, let's calculate the torque:
Torque = Force x distance
Torque = 0.98 N x 0.45 m
Torque = 0.441 Nm
Since the distance of the 0.1 kg mass is on one side of the ruler, the balanced torque on the other side needs to be the same. Therefore, we can write:
Torque = Force x distance
0.441 Nm = mass x 0.205 m
Solving for mass:
mass = 0.441 Nm / 0.205 m
mass ≈ 2.15 kg
Therefore, a mass of approximately 2.15 kg is required to balance the meter rule.
To find the mass required to balance the meter rule, we can use 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 must be equal to the sum of the anticlockwise moments about the same point.
In this case, we need to find the mass that will balance the meter rule when one mass is hanging at a distance of 20.5cm from the center, and another mass of 0.1kg is hanging at a distance of 45cm from the center.
Let's assume the mass required to balance the meter rule is "m" (in kg).
The clockwise moment of the 0.1kg mass is given by:
Clockwise Moment = (0.1kg) * (45cm)
The anticlockwise moment of the mass at 20.5cm is given by:
Anticlockwise Moment = (m) * (20.5cm)
Since these moments need to balance each other for equilibrium, we can set up the following equation:
Clockwise Moment = Anticlockwise Moment
(0.1kg) * (45cm) = (m) * (20.5cm)
Now, let's solve for "m":
0.1 * 45 = m * 20.5
4.5 = m * 20.5
m = 4.5 / 20.5
m ≈ 0.22 kg
Therefore, the mass required to balance the meter rule is approximately 0.22 kg.