GATE ME 2019 Set 1 — Question 39
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Engineering Mechanics → Dynamics → Dynamics of Rigid Bodies
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Question
A car having weight is moving forward, in the direction from the rear wheels towards the front wheels (to the right in the figure). The center of gravity (CG) of the car is located at height from the ground, midway between the front and rear wheels. The distance between the front and rear wheels is . The acceleration of the car is in the direction of motion, and acceleration due to gravity is . The reactions on the front wheels () and rear wheels () are given by
Correct answer
(C) R_f = (W)/(2) - (W)/(g) ((h)/(l)) a; Rᵣ = (W)/(2) + (W)/(g) ((h)/(l)) a
Solution
Use d'Alembert's principle: add the inertia force at the CG, acting backwards (opposite to the motion, towards the rear wheels), at height .
1.Vertical equilibrium: .
2.Moments about the rear-wheel contact point (front wheel is at distance , CG at ):
3.Then .
Forward acceleration transfers load from the front wheels to the rear wheels.- (A) and (D) give equal reactions, which ignores the load transfer.
- (B) has the transfer in the wrong direction (that would be braking).
- (C) matches.
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