Question 1

If an elephant grows to twice its normal height,its weight will be multiplied by about

Accepted Answer

The weight of an object is proportional to its volume. If the height doubles, the volume (and thus the weight) increases by a factor of 2^3 = 8, assuming the shape remains similar.

Question 2

When a living cell doubles in diameter,the amount of its material to be nourished is multiplied by eight,but the amount of membrane through which to feed it is multiplied by

Accepted Answer

When a cell doubles in diameter, its volume is multiplied by 8 (2^3) but its surface area is only multiplied by 4 (2^2). This means that the amount of membrane through which the cell needs to be nourished is only multiplied by 4, not 8. Therefore, the best choice is B.

Question 3

If an elephant grew to twice its height,the area of its ears would be about

Accepted Answer

The area of an object scales with the square of its linear dimensions. If the height (a linear dimension) doubles, the area of the ears would increase by a factor of four (2^2).

Question 4

Which cooks faster in boiling oil?

Accepted Answer

A sliced potato cooks faster in boiling oil because it has a larger surface area exposed to the heat, allowing it to cook more quickly than a whole potato.

Question 5

A weightless spring is stretched 10 cm by a suspended 1-kg block.If two such springs are used to suspend the block,one spring above the other,to effectively provide one double-length spring,then the total stretch of the double-length spring will be

Accepted Answer

The spring constant of a spring is given by k = F/x, where F is the force applied and x is the displacement or stretch. Therefore, if one spring is stretched by 10 cm due to the weight of a 1-kg block, the spring constant of that spring can be found as follows:

k1 = F/x = (1 kg) * (9.8 m/s^2) / (0.1 m) = 98 N/m.

When two identical springs are used in parallel, the effective spring constant is simply the sum of the individual spring constants, i.e., k_eff = 2k1 = 196 N/m. The stretch of the double-length spring can be found by using Hooke's law:

F = k_eff * x_eff,

where x_eff is the stretch of the double-length spring. When the 1-kg block is suspended using the double-length spring, the force applied is simply the weight of the block, i.e., F = (1 kg) * (9.8 m/s^2) = 9.8 N. Therefore,

x_eff = F / k_eff = (9.8 N) / (196 N/m) = 0.05 m = 5 cm.

Therefore, the total stretch of the double-length spring is 2*x_eff = 2*(5 cm) = 10 cm.

Question 6

A dome-shaped house is more heat efficient than a rectangular house because a dome has

Accepted Answer

A dome shape has a smaller surface area relative to its volume compared to a rectangular shape, which reduces heat loss and makes it more heat efficient.

Question 7

Use the following figure to answer the question: 
-A spring is stretched 10 cm by a suspended 1-kg block.If two such springs side-by-side are used to suspend the block,so each spring supports half the weight of the block,then each spring will stretch

Accepted Answer

When one spring supports the 1-kg block, it stretches 10 cm. This means that the spring constant, k, is:

F = kx

where F is the force applied by the spring (in newtons), and x is the displacement of the spring from its equilibrium position (in meters).

For a 1-kg block hanging from the spring, the weight of the block is:

Fg = mg = (1 kg)(9.8 m/s^2) = 9.8 N

Since the spring is stretched 10 cm (or 0.1 m), we can solve for k:

9.8 N = k(0.1 m)
k = 98 N/m

Now, if we use two springs side-by-side, each spring must support half the weight of the block (or 4.9 N). The displacement of each spring can be found by solving:

4.9 N = kx

where k is still 98 N/m (since the springs are the same), and x is the displacement we're solving for. Rearranging this equation, we get:

x = 4.9 N / 98 N/m
x = 0.05 m

Converting this back to centimeters, we get:

x = 5 cm

Therefore, each spring will stretch 5 cm when supporting half the weight of the block.

Question 8

Which potatoes when peeled produce the most peelings?

Accepted Answer

Small potatoes have a higher surface area to volume ratio compared to large potatoes, meaning that when peeled, they will produce more peelings for the same weight of potatoes. Therefore, 10 kg of small potatoes will produce more peelings compared to 10 kg of large potatoes.

Question 9

Tripling the linear size of an object multiplies its area by

Accepted Answer

Since the linear size is tripled, the area will be multiplied by 3^2 = 9, because the area is proportional to the square of the linear dimension. Similarly, the volume is proportional to the cube of the linear dimension, so tripling the linear size multiplies the volume by 3^3 = 27. Therefore, option C is correct, which states that the area is multiplied by 9, and its volume is multiplied by 27.

Question 10

Which geometrical shape has the least surface area for a given volume?

Accepted Answer

Sphere has the smallest surface area to volume ratio out of all the given options. This is due to the fact that a sphere has the smallest surface area for a given volume compared to other shapes.

Question 11

An elephant eats less for its size than smaller animals because

Accepted Answer

Larger animals like elephants have a smaller surface area to volume ratio, meaning they lose less heat relative to their size and thus require less food per unit of body mass compared to smaller animals.

Question 12

A kilogram of peaches have more skin area than a kilogram of

Accepted Answer

Grapefruits are much larger than peaches, so a kilogram of grapefruits would have fewer individual fruits and therefore less total skin area compared to a kilogram of smaller fruits like peaches.

Question 13

An unstretched hanging spring is 50 cm long.Suspending a 100-N weight from it makes its length 60 cm.Adding another 100-N weight will make the spring's length

Accepted Answer

The answer of An unstretched hanging spring is 50 cm...

Question 14

Which has more skin compared to its body weight,an elephant or a mouse?

Accepted Answer

A mouse has more skin relative to its body weight compared to an elephant. This is because smaller animals generally have a higher surface area to volume ratio.

Question 15

A metal block has a density of 5000 kg per cubic meter and a mass of 15,000 kg.What is its volume?

Accepted Answer

The answer of A metal block has a density of...

Question 16

A metal block has a density of 5000 kg per cubic meter and a volume of 2 cubic meters.What is the block's mass?

Accepted Answer

The formula for finding mass is: 
mass = density x volume
Substituting the given values:
mass = 5000 kg/m^3 x 2 m^3
mass = 10,000 kg
Therefore, the mass of the metal block is 10,000 kg. The correct answer is D.

Question 17

Suppose all sized potatoes are selling at the same price per kilogram.If you peel them for mashing,you will get more potato for your money if you buy

Accepted Answer

The larger the potato, the smaller the amount of peel relative to the amount of usable potato. This means that even though you may pay the same price per kilogram for all sizes of potatoes, the larger potatoes will give you more usable potato for your money after peeling. Therefore, choosing the largest potatoes will give you the most potato for your money.

Question 18

Which has more skin,an elephant or a mouse?

Accepted Answer

Elephants have much more skin than mice due to their large size.

Question 19

A solid glass ball weighs 1 newton.One with twice the diameter weighs

Accepted Answer

The weight of the ball is proportional to its volume, which is proportional to the cube of its diameter. Doubling the diameter increases the volume (and thus the weight) by a factor of 2^3 = 8, so the new weight is 8 N, which is more than 4 N.

Question 20

Doubling the linear size of an object multiplies its area by

Accepted Answer

When the linear size of an object is doubled, its area will be multiplied by 4 (2^2) and its volume will be multiplied by 8 (2^3). Therefore, option B is the correct choice.

Quiz 12: Solids