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A weighing machine consists of a 2 kg pan resting on spring. In this condition, with the pan resting on the spring, the length of the spring is 200 mm. When a mass of 20 kg is placed on the pan, the length of the spring becomes 100 mm. For the spring, the undeformed length lo and the spring constant k (stiffness) are:
[GATE-2005]
  • a)
    lo = 220 mm, k = 1862 N/m
  • b)
    lo = 210 mm, k = 1960 N/m
  • c)
    lo = 200 mm, k = 1960 N/m
  • d)
    lo = 200 mm, k = 2156 N/m
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A weighing machine consists of a 2 kg pan resting on spring. In this c...
Initial length = lo m and stiffness = k N/m
Just solve the above equations.
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Most Upvoted Answer
A weighing machine consists of a 2 kg pan resting on spring. In this c...
To solve this problem, we can use Hooke's Law, which states that the force exerted by a spring is proportional to the displacement from its equilibrium position. Mathematically, this can be expressed as F = kx, where F is the force, k is the spring constant, and x is the displacement.

Let's analyze the given information step by step:

Step 1: Determine the displacement of the spring when a 20 kg mass is placed on the pan.
The displacement of the spring can be calculated by subtracting the length of the spring with the mass on it from the length of the spring when it is at rest.

Displacement = 200 mm - 100 mm = 100 mm = 0.1 m

Step 2: Calculate the force exerted by the spring when the 20 kg mass is placed on the pan.
The force exerted by the spring can be calculated using Hooke's Law:

F = kx

where F is the force, k is the spring constant, and x is the displacement.

Plugging in the values, we have:

F = k * 0.1

Step 3: Calculate the force exerted by the 20 kg mass.
The force exerted by the 20 kg mass can be calculated using the formula:

F = mg

where F is the force, m is the mass, and g is the acceleration due to gravity.

Plugging in the values, we have:

F = 20 kg * 9.8 m/s^2 = 196 N

Step 4: Equate the forces exerted by the spring and the 20 kg mass.
Since the force exerted by the spring is equal to the force exerted by the 20 kg mass, we can set up the equation:

F = k * 0.1 = 196 N

Solving for k, we have:

k = 196 N / 0.1 = 1960 N/m

Therefore, the spring constant is 1960 N/m.

Step 5: Determine the undeformed length of the spring.
The undeformed length of the spring can be calculated by subtracting the displacement caused by the 20 kg mass from the length of the spring when it is at rest.

Undeformed length = 200 mm - 100 mm = 100 mm = 0.1 m

Therefore, the undeformed length of the spring is 0.1 m.

Hence, the correct answer is option B: lo = 210 mm, k = 1960 N/m.
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A weighing machine consists of a 2 kg pan resting on spring. In this condition, with the pan resting on the spring, the length of the spring is 200 mm. When a mass of 20 kg is placed on the pan, the length of the spring becomes 100 mm. For the spring, the undeformed length lo and the spring constant k (stiffness) are:[GATE-2005]a)lo = 220 mm, k = 1862 N/mb)lo = 210 mm, k = 1960 N/mc)lo = 200 mm, k = 1960 N/md)lo = 200 mm, k = 2156 N/mCorrect answer is option 'B'. Can you explain this answer?
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A weighing machine consists of a 2 kg pan resting on spring. In this condition, with the pan resting on the spring, the length of the spring is 200 mm. When a mass of 20 kg is placed on the pan, the length of the spring becomes 100 mm. For the spring, the undeformed length lo and the spring constant k (stiffness) are:[GATE-2005]a)lo = 220 mm, k = 1862 N/mb)lo = 210 mm, k = 1960 N/mc)lo = 200 mm, k = 1960 N/md)lo = 200 mm, k = 2156 N/mCorrect answer is option 'B'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A weighing machine consists of a 2 kg pan resting on spring. In this condition, with the pan resting on the spring, the length of the spring is 200 mm. When a mass of 20 kg is placed on the pan, the length of the spring becomes 100 mm. For the spring, the undeformed length lo and the spring constant k (stiffness) are:[GATE-2005]a)lo = 220 mm, k = 1862 N/mb)lo = 210 mm, k = 1960 N/mc)lo = 200 mm, k = 1960 N/md)lo = 200 mm, k = 2156 N/mCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A weighing machine consists of a 2 kg pan resting on spring. In this condition, with the pan resting on the spring, the length of the spring is 200 mm. When a mass of 20 kg is placed on the pan, the length of the spring becomes 100 mm. For the spring, the undeformed length lo and the spring constant k (stiffness) are:[GATE-2005]a)lo = 220 mm, k = 1862 N/mb)lo = 210 mm, k = 1960 N/mc)lo = 200 mm, k = 1960 N/md)lo = 200 mm, k = 2156 N/mCorrect answer is option 'B'. Can you explain this answer?.
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