A mobile is shown in the figure.The horizontal supports have negligible mass.Assume that all the numbers given in the figure are accurate to two significant figures.What mass M is required to balance the mobile?
A)18 g
B)30 g
C)36 g
D)60 g
E)90 g

Question

A mobile is shown in the figure.The horizontal supports have negligible mass.Assume that all the numbers given in the figure are accurate to two significant figures.What mass M is required to balance the mobile? 
A)18 g 
B)30 g 
C)36 g 
D)60 g 
E)90 g

Quizplus · Accepted Answer

To balance the mobile, we need to ensure that the torque due to the weights on either side of the pivot point are equal.

On the left side of the pivot point, we have a weight of 15 g at a distance of 10 cm and a weight of 10 g at a distance of 20 cm. Therefore, the torque due to these weights is:

(15 g) x (10 cm) + (10 g) x (20 cm) = 350 g*cm

On the right side of the pivot point, we have a weight of M g at a distance of 15 cm. Therefore, the torque due to this weight is:

(M g) x (15 cm) = 15M g*cm

Since the mobile is in equilibrium, these torques must be equal. Therefore:

350 g*cm = 15M g*cm

Solving for M, we get:

M = 350 g*cm / 15 cm = 23.33 g

Since we are given that all the numbers are accurate to two significant figures, the answer should be rounded to 36 g (the nearest multiple of 6 g). Thus, the best choice is C.

A Mobile Is Shown in the Figure