A balanced lever has two weights on it, the first with mass #6 kg # and the second with mass #45 kg#. If the first weight is # 9 m# from the fulcrum, how far is the second weight from the fulcrum?

Answer 1

#d=1.2m#

A body which has no tendency to rotate under the combined result of a number of forces acting on it is called to be a balanced state.

The rotational tendency of a force is called Moment of the force.

Moment #=#Force# times #Distance#=F times D#
where #D# is the length of Moment arm, which is perpendicular distance between the line of action of the force and the center of moments.

Also in a balanced lever clockwise moments are equal to clockwise moments.

In the given question, forces acting are two weights for which #F=m.g# where #g# is acceleration due to gravity.
If #d# is the length of Moment arm, i.e ., perpendicular distance between the weight and the fulcrum, then moment of one force about the fulcrum is equal and opposite to the moment of other force about the fulcrum.
Stating mathematically #Moment_1=Moment_2#
or # m_1.g.d_1=m_2.g.d_2# #implies m_1.d_1=m_2.d_2#
Inserting given values # 6 times 9=45.d_2# or # d_2=(6 times 9)/45 m#
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Answer 2

Using the principle of moments for a balanced lever:

[ \text{Moment of first weight} = \text{Moment of second weight} ]

[ (6 \text{ kg}) \times (9 \text{ m}) = (45 \text{ kg}) \times (\text{distance of second weight from fulcrum}) ]

[ 6 \times 9 = 45 \times (\text{distance of second weight from fulcrum}) ]

[ \text{Distance of second weight from fulcrum} = \frac{6 \times 9}{45} ]

[ \text{Distance of second weight from fulcrum} = \frac{54}{45} ]

[ \text{Distance of second weight from fulcrum} = 1.2 \text{ meters} ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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