GATE 2021 ME (ME2) – Question 62

Engineering Mechanics · Kinematics and dynamics of rigid bodies in plane motion · 2 marks · Numerical answer

The wheels and axle system lying on a rough surface is shown in the figure. Each wheel has diameter 0.8 m and mass 1 kg. Assume that the mass of the wheel is concentrated at rim and neglect the mass of the spokes. The diameter of axle is 0.2 m and its mass is 1.5 kg. Neglect the moment of inertia of the axle and assume $g=9.8$ m/s². An effort of 10 N is applied on the axle in the horizontal direction shown at mid span of the axle. Assume that the wheels move on a horizontal surface without slip. The acceleration of the wheel axle system in horizontal direction is _____ m/s² (round off to one decimal place).

Two rim-mass wheels of diameter 0.8 m on an axle of diameter 0.2 m; a 10 N force acts horizontally at the lower axle tangent. See the attached source image.

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Correct answer: 1.39 to 1.41

Explanation

Total translating mass is M=3.5 kg and wheel inertia is I=2(1)(0.4)²=0.32 kg m². The effort acts 0.1 m below the centre, producing torque opposite the clockwise rolling acceleration.

Eliminating ground friction using a=Rα gives $a=F(1-r/R)/(M+I/R^2)=10(1-0.1/0.4)/(3.5+2)=1.36364$. **Answer: 1.4 m/s²**.