The GATE Grind

GATE 2019 ME (ME1) – Question 39

Engineering Mechanics · Kinematics and dynamics of rigid bodies in plane motion · 2 marks · Multiple choice

A car of weight W accelerates at a in the shown direction. Its centre of gravity is height h above ground, midway between front and rear axles separated by l. With gravity g, find front and rear normal reactions Rf and Rr.

Diagram for GATE 2019 ME (ME1) question 39
  1. $R_f=R_r=W/2-Wah/(gl)$
  2. $R_f=W/2+Wah/(gl),\ R_r=W/2-Wah/(gl)$
  3. $R_f=W/2-Wah/(gl),\ R_r=W/2+Wah/(gl)$
  4. $R_f=R_r=W/2+Wah/(gl)$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (C) $R_f=W/2-Wah/(gl),\ R_r=W/2+Wah/(gl)$

Explanation

Vertical equilibrium gives $R_f+R_r=W$. The inertial force $Wa/g$ at height $h$ transfers load $Wah/(g\ell)$ from front to rear. Thus **$R_f=W/2-Wah/(g\ell)$ and $R_r=W/2+Wah/(g\ell)$, C**.