Imagine a balance beam with unequal arms. An earring placed in the left basket was balanced by 4.71 g of standard masses on the right. When placed in the right basket, the same earring required 14.66 g on the left to balance.

(a) Which was the longer arm?

(b) What is the mass of the earring?

Question

Imagine a balance beam with unequal arms. An earring placed in the left basket was balanced by 4.71 g of standard masses on the right. When placed in the right basket, the same earring required 14.66 g on the left to balance. 

(a) Which was the longer arm?
  
(b) What is the mass of the earring?

ranga · Answer

Let the left arm be 1 unit long and the right arm be x units long.
Let M be the mass of the earring.
When earring is placed on the left:    M * 1 = 4.71 * x     ----- (1)
When earring is placed on the right:  M * x = 14.66 * 1   ----- (2)
Divide second equation by the first:
x / 1 = 14.66 / (4.71x)
x^2 = 14.66/4.71 = 3.1125
x = 1.76.  
Left arm is 1 unit and right arm is 1.76 units.  So the right arm is longer

A)  The right arm is longer.

B) Put x = 1.76 in (1):  M = 4.71 * 1.76 = 8.31 grams.