Question 50

P will be multiplied by 8.

When the values of V and G are each doubled, the value of P will increase by a factor of 8, as P is proportional to the square of V and directly proportional to G in the formula P = V^2 * G.

A) unchanged

This option is incorrect because if V and G are both doubled, P will not remain the same. Instead, it will experience an increase based on the changes to V and G.

B) multiplied by 2

This option is also incorrect. Doubling V results in V^2 increasing by a factor of four (since (2V)^2 = 4V^2), and simply doubling G would not result in just doubling P. Therefore, P cannot be multiplied by only 2.

C) multiplied by 4

This option fails to account for the effect of doubling both V and G. While doubling V alone would yield a fourfold increase in P due to V^2, G must also be considered. Since G is also doubled, P is actually multiplied by 8, not just 4.

D) multiplied by 8

This option is correct because when both V and G are doubled, P = (2V)^2 * (2G) = 4V^2 * 2G = 8 * (V^2 * G), indicating that P increases by a factor of 8.

E) multiplied by 16

This option is incorrect because while it might seem logical to consider the effects of doubling V and G as independent factors, the mathematical relationship shows that P is not multiplied by 16. Instead, the factor is 8 as detailed in the calculations.

Conclusion

The correct answer is D, as when both V and G are doubled, the resulting value of P reflects the combined effects of these changes, resulting in an eightfold increase. All other options fail to accurately represent the mathematical relationship defined in the formula P = V^2 * G.