IMU Question 4 The thrust $$ T $$ of a propeller varies jointly as the square of the number $$ n $$ of revolutions per second and the fourth power of its diameter $$ d $$. What is the effect on $$ T $$ if $$ n $$ is doubled and $$ d $$ is halved? ( 3 marks)

Question

UpStudy AI · Accepted Answer

Given that the thrust $$ T $$ varies jointly as the square of the number of revolutions per second $$ n $$ and the fourth power of the diameter $$ d $$, we can express this relationship as:

$$
T = k \cdot n^2 \cdot d^4
$$

where $$ k $$ is the constant of variation.

**Effect of Doubling $$ n $$ and Halving $$ d $$:**

1. **Doubling $$ n $$:**
   $$
   n_{\text{new}} = 2n
   $$
   $$
   (n_{\text{new}})^2 = (2n)^2 = 4n^2
   $$

2. **Halving $$ d $$:**
   $$
   d_{\text{new}} = \frac{d}{2}
   $$
   $$
   (d_{\text{new}})^4 = \left(\frac{d}{2}\right)^4 = \frac{d^4}{16}
   $$

3. **New Thrust $$ T_{\text{new}} $$:**
   $$
   T_{\text{new}} = k \cdot (4n^2) \cdot \left(\frac{d^4}{16}\right) = k \cdot \frac{4n^2 d^4}{16} = \frac{k n^2 d^4}{4} = \frac{T}{4}
   $$

**Conclusion:**
When the number of revolutions per second is doubled and the diameter is halved, the thrust $$ T $$ is reduced to one fourth of its original value.

**Answer:**  
Its thrust becomes one fourth as large. The thrust is reduced by a factor of four.
When the number of revolutions per second is doubled and the diameter is halved, the thrust becomes one fourth as large.

IMU
Question 4
The thrust of a propeller varies jointly as the square of the number of revolutions per second
and the fourth power of its diameter . What is the effect on if is doubled and is halved?
( 3 marks)

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IMU Question 4 The thrust of a propeller varies jointly as the square of the number of revolutions per second and the fourth power of its diameter . What is the effect on if is doubled and is halved? ( 3 marks)