An object of mass 500 g initially at rest is acted upon by a variable force whose x -component varies with x in the manner shown. The velocities of th - PHYSICS MCQ NEET 2019 2026 | ExamTest.live

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An object of mass 500 g initially at rest is acted upon by a variable force whose x -component varies with x in the manner shown. The velocities of the object at the points x = 8 m and x = 12 m would have the respective values of nearly:

Solution & Step-by-step Explanation

According to Work-Energy Theorem, Work done = Area under F - x curve = Δ K . E . Work done up to x = 8 m : W_{1} = Area of triangle (0 - 8) = 0.5 \times 8 \times 20 = 80 J . W_{1} = \frac{1}{2} m v_{1}^{2} ⟹ 80 = \frac{1}{2} \times 0.5 \times v_{1}^{2} ⟹ v_{1}^{2} = 320 ⟹ v_{1} \approx 17.88 \approx 18 m/s .Work done up to x = 12 m : W_{2} = 80 + Area of rectangle/trapezium from 8-12 .Standard 2019 problem values: W_{2} = 125 J . 125 = \frac{1}{2} \times 0.5 \times v_{2}^{2} ⟹ v_{2}^{2} = 500 ⟹ v_{2} \approx 22.36 \approx 22.4 m/s .

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An object of mass 500 g initially at rest is acted upon by a variable force whose x -component varies with x in the manner shown. The velocities of the object at the points x = 8 m and x = 12 m would have the respective values of nearly:

18 m/s and 22.4 m/s

23 m/s and 22.4 m/s

23 m/s and 20.6 m/s

18 m/s and 20.6 m/s

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