Finding True Weight with False Balance

[zorro]

Homework Statement

A body weighs 6 gms when placed in one pan and 24 gms when placed on the other pan of a false balance. If the beam is horizontal when both the pans are empty, the true weight of the body is :

Homework Equations

The Attempt at a Solution

I don't know which concept(s) are involved.
Is it something related to 'Torque' concept ?

 

[hikaru1221]

You only need the basic concept of torque balance.
I think the situation is like this: you place the body on one pan and some weights on the other pan such that the beam is horizontal. So the "weight" of the body = the total weight of the weights placed on the other pan.
From that, write down 2 equations for torque balance. Notice that the pans also create torques & as the question states, the beam is horizontal when the pans are empty

 

[rl.bhat]

Homework Statement

A body weighs 6 gms when placed in one pan and 24 gms when placed on the other pan of a false balance. If the beam is horizontal when both the pans are empty, the true weight of the body is :

Homework Equations

The Attempt at a Solution

I don't know which concept(s) are involved.
Is it something related to 'Torque' concept ?

In false balance,the fault may be either the weight of the pans are not equal or the fulcrum is not on the center of mass or the both. Since the pan is horizontal when both the pans are empty, both the faults must be there in the balance.
If W1 and W2 are the weighs of the pans, and W0 is the true weight of the object and x is the distance between the fulcrum and the CM, then
(W1)(l+x) = (W2)(l-x) ...(1)
(W1+6)(l+x) = (W0+W2)(l-x) ...(2)
(W1+W0)(l+x) = (24+W2)(l-x) ...(3)
Can you proceed from here on?

 

[zorro]

Is it not 6g and 7g?
What type of balance is this? Is it the 'old 2 pans' balance? If yes then how can it measure so small weight?

 

[rl.bhat]

Is it not 6g and 7g?
What type of balance is this? Is it the 'old 2 pans' balance? If yes then how can it measure so small weight?

Yes. It is old 2 pan balance and true weight is sqrt(6*24).