Question:
The force constant of weightless spring is 16 N/m. A body of mass 1.0 kg suspended from it is pulled down through 5 cm and then released. The maximum kinetic energy of the system (spring + body) will be:
The force constant of weightless spring is 16 N/m. A body of mass 1.0 kg suspended from it is pulled down through 5 cm and then released. The maximum kinetic energy of the system (spring + body) will be:
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The maximum kinetic energy in a spring-mass system is equal to the potential energy stored in the spring at maximum displacement.
Updated On: Apr 22, 2026
- \( 2 \times 10^{-2} \, \text{J} \)
- \( 4 \times 10^{-2} \, \text{J} \)
- \( 8 \times 10^{-2} \, \text{J} \)
- \( 16 \times 10^{-2} \, \text{J} \)
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The Correct Option is A
Solution and Explanation
Step 1: Understand the energy in the spring-mass system.
In a spring-mass system, the maximum kinetic energy is equal to the maximum potential energy stored in the spring when it is stretched or compressed. The potential energy in the spring is given by: \[ U = \frac{1}{2} k x^2 \] where: - \( k \) is the spring constant, and - \( x \) is the displacement from the equilibrium position.
Step 2: Calculate the potential energy.
Here, the spring constant \( k = 16 \, \text{N/m} \), and the displacement \( x = 5 \, \text{cm} = 0.05 \, \text{m} \). Substituting the values into the formula for potential energy: \[ U = \frac{1}{2} \times 16 \times (0.05)^2 = 2 \times 10^{-2} \, \text{J} \]
Step 3: Conclusion.
The maximum kinetic energy of the system is \( 2 \times 10^{-2} \, \text{J} \), which is option (1).
In a spring-mass system, the maximum kinetic energy is equal to the maximum potential energy stored in the spring when it is stretched or compressed. The potential energy in the spring is given by: \[ U = \frac{1}{2} k x^2 \] where: - \( k \) is the spring constant, and - \( x \) is the displacement from the equilibrium position.
Step 2: Calculate the potential energy.
Here, the spring constant \( k = 16 \, \text{N/m} \), and the displacement \( x = 5 \, \text{cm} = 0.05 \, \text{m} \). Substituting the values into the formula for potential energy: \[ U = \frac{1}{2} \times 16 \times (0.05)^2 = 2 \times 10^{-2} \, \text{J} \]
Step 3: Conclusion.
The maximum kinetic energy of the system is \( 2 \times 10^{-2} \, \text{J} \), which is option (1).
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