A meter rule is placed horizontally at a fixed point while mass are suspended at both right and left hands of the ruler from the center of the ruler is hung 20cm away from the center and a mass of 20kg is hung at the other side from the center at distance 30cm.find the mass required to balance the ruler

Question

A meter rule is placed horizontally at a fixed point while mass are suspended at both right and left hands of the ruler from the center of the ruler is hung 20cm away from the center and a mass of 20kg is hung at the other side from the center at distance 30cm.find the mass required to balance the ruler

Answer 1

Why did the ruler bring a scale to the weight-lifting competition? It wanted to find its perfect match!

Well, for the ruler to be balanced, the moments on both sides of the center must be equal.

Now, let's calculate the moments. The moment on the left side is calculated as the distance (20 cm) multiplied by the mass (let's call it M) on that side. The moment on the right side is calculated as the distance (30 cm) multiplied by the mass (20 kg) on that side.

So, the equation becomes:

20 cm * M = 30 cm * 20 kg

Now, let's solve it:

20M = 600

M = 600/20

M = 30 kg

So, to balance the ruler, a mass of 30 kg is required on the left side.

Answer 2

To balance the ruler, the sum of the torques on each side of the ruler must be equal. The torque is calculated by multiplying the force by the perpendicular distance from the pivot point.

Let's assume the center of the ruler as the pivot point. The torque on the left side is calculated as follows:

Torque_left = Force_left * Distance_left

Torque_left = Mass_left * gravity * Distance_left

Similarly, the torque on the right side is calculated as follows:

Torque_right = Force_right * Distance_right

Torque_right = Mass_right * gravity * Distance_right

We know that the torques on both sides must be equal for the ruler to be balanced. Therefore:

Torque_left = Torque_right

Mass_left * gravity * Distance_left = Mass_right * gravity * Distance_right

Now let's substitute the given values:

Mass_left * 9.8 * 20cm = 20kg * 9.8 * 30cm

Simplifying the equation:

Mass_left * 20 = 20kg * 30

Mass_left = (20kg * 30) / 20

Mass_left = 30kg

Therefore, a mass of 30kg is required to balance the ruler.

Answer 3

To find the mass required to balance the ruler, we need to use the principle of moments. Moments refer to the turning effect of a force about a pivot point. In this case, the pivot point is the fixed point where the meter rule is placed horizontally.

To balance the ruler, the total clockwise moment must be equal to the total anticlockwise moment.

Let's calculate the moments caused by the masses at both ends of the ruler:

Mass at 20cm (left side):
Moment = Mass x Distance from pivot
Moment1 = (Mass1) x (0.2m)

Mass at 30cm (right side):
Moment = Mass x Distance from pivot
Moment2 = (Mass2) x (0.3m)

Since the ruler is balanced, the two moments must be equal:
Moment1 = Moment2

(Mass1) x (0.2m) = (Mass2) x (0.3m)

Now we can solve for Mass1:

Mass1 = (Mass2 x 0.3m) / 0.2m

Substituting the given values:
Mass1 = (20kg x 0.3m) / 0.2m
Mass1 = 30kg

Therefore, to balance the ruler, a mass of 30kg is required.