GATE AE 2022 • Q39 MCQ • 2 Marks Engineering Mathematics

Engineering Mathematics

Differential Equations

Subtopic: First Order ODEs

Question Statement:

A cylindrical object of diameter $900\text{ mm}$ is designed to move axially in air at $60\text{ m/s}$. Its drag is estimated on a geometrically half-scaled model in water. Coefficients of dynamic viscosity and densities for air and water are $1.86 \times 10^{-5}\text{ Pa}\cdot\text{s}, 1.2\text{ kg/m}^3$ and $1.01 \times 10^{-3}\text{ Pa}\cdot\text{s}, 1000\text{ kg/m}^3$ respectively. Drag measured for the model is $2280\text{ N}$. Drag experienced by the full-scale object is _____ $\text{N}$ (rounded off to the nearest integer).
Question figure for GATE AE 2022 Q39

Scientific schematic diagram reproduced from official IIT paper

Options:

  • (A) 322
  • (B) 644
  • (C) 1288
  • (D) 2576

Official Answer Key:

B

Step-by-Step Solution & Explanation

### **Detailed Step-by-Step Solution (GATE AE 2022 Q.39)** **1. Dynamic Similarity via Reynolds Number**: $$Re_m = Re_p \implies \frac{\rho_m V_m D_m}{\mu_m} = \frac{\rho_p V_p D_p}{\mu_p}$$ With $D_m / D_p = 0.5$: $$V_m = V_p \left(\frac{D_p}{D_m}\right) \left(\frac{\rho_p}{\rho_m}\right) \left(\frac{\mu_m}{\mu_p}\right)$$ **2. Drag Force Scaling**: $$\frac{D_{\text{drag}, p}}{D_{\text{drag}, m}} = \frac{\rho_p V_p^2 D_p^2}{\rho_m V_m^2 D_m^2}$$ Evaluating yields $D_{\text{drag}, p} \approx 644\text{ N}$. - **Official Answer Key**: **B**
← Previous (Q38) All 2022 Questions Next (Q40) →

Related Differential Equations Solved Questions

View All Differential Equations PYQs →
GATE AE 2026 Q49 NAT • 2M

Consider the differential equation with the initial conditions given below. If y(x) is the solution of the equation, the value of the slope, $\frac{dy}{dx}$ , at x = ln(2) is ________ (rounded off to three decimal places). $\frac{d^2y}{dx^2}$ + 2 $\frac{dy}{dx}$ + y = 0 with y|x=0 = 0 and $\frac{dy}{dx}$| x=0 = 1
GATE AE 2025 Q14 MCQ • 1M

The partial differential equation $\frac{\partial^2 u}{\partial x^2} + 4\frac{\partial^2 u}{\partial x\partial y} + 2\frac{\partial^2 u}{\partial y^2} = 0$ is:
GATE AE 2025 Q43 NAT • 2M

Consider the ordinary differential equation: $\frac{1}{2} \frac{dy}{dx} + \frac{y}{x} = 1$. If $y = 2/3$ at $x = 1$, then the value of $y$ at $x = 3$ is ______ (rounded off to the nearest integer).
GATE AE 2024 Q12 MCQ • 1M

The acceleration of a body travelling in a straight line is given by $a = -C_1 - C_2 v^2$, where $v$ is the velocity, and $C_1, C_2$ are positive constants. Starting with an initial positive velocity $v_0$, the distance travelled by the body before coming to rest for the first time is:

Practice This in Real CBT Exam Interface

Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.

Launch CBT Mock Test