Chapter 13, Problem 71A

(a)

To determine

Reading on the scale if $8N$ is weight is added.

Answer to Problem 71A

The scale reads $203N$ after $8N$ rock sinks in the aquarium.

Explanation of Solution

Given:

Weight of the aquarium, $W_a=195N$

Weight of the rock, $W_r=8N$

Formula used:

  $F_g=W_a+W_r$

Here, ${\text{W}}_{\text{a}}$ is the weight of the aquarium and ${\text{W}}_{\text{r}}$ is the weight of the book.

Calculation:

After $8N$ rock is added to the aquarium, and the rock sinks, the total weight of the aquarium becomes:

  $F_g=195N+8N=203N$

This is because the buoyant force is equal to the weight of the water displaced by adding the rock.

Conclusion: After $8N$ rock is added to the aquarium, total weight of the aquarium becomes $203N$ .

(b)

To determine

Reading on the scale if $2N$ is weight is added.

Answer to Problem 71A

The scale reads $197N$ after $2N$ fish is added to the aquarium and the rock is removed.

Explanation of Solution

Given: Weight of the aquarium, $W_a=195N$

Weight of the rock, $W_r=8N$

Formula used:

Since, the rock is removed, and a fish is added to the aquarium:

  $F_g=W_a+W_f$

Here, ${\text{W}}_{\text{a}}$ is the weight of the aquarium and ${\text{W}}_{\text{f}}$ is the weight of the fish.

Calculation:

After $2N$ rock is added to the aquarium, and the rock sinks, the total weight of the aquarium becomes:

  $F_g=195N+2N=197N$

This is because the buoyant force is equivalent to the weight of the water displaced by putting the rock.

Conclusion: After $2N$ fish is added to the aquarium, total weight of the aquarium becomes $197N$ .