Work Energy Theorem
Question

# A sphere of mass 2 kg is moving on a frictionless horizontal table with velocity v. It strike with a spring of constant 1 N/m and compresses it by 4 m. The velocity (v) of the sphere is :

Moderate
Solution

## As per work energy theorem  ${\mathrm{w}}_{\mathrm{sp}}=\mathrm{\Delta K}.\mathrm{E}$$⇒\frac{1}{2}{\mathrm{Kx}}^{2}=\frac{1}{2}{\mathrm{mv}}^{2}$$⇒\mathrm{v}=\sqrt{\frac{\mathrm{K}}{\mathrm{m}}}\mathrm{x}$$=\sqrt{\frac{1}{2}}.4=2\sqrt{2}\text{\hspace{0.17em}}\mathrm{m}/\mathrm{s}$

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The passage contains a physics problem involving the Work Energy Theorem, where a sphere compresses a spring, and the velocity of the sphere is to be determined. The solution to the problem is provided, showing the calculation of the velocity.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
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- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Work Energy Theorem
Question

# A sphere of mass 2 kg is moving on a frictionless horizontal table with velocity v. It strike with a spring of constant 1 N/m and compresses it by 4 m. The velocity (v) of the sphere is :

Moderate
Solution

## As per work energy theorem  ${\mathrm{w}}_{\mathrm{sp}}=\mathrm{\Delta K}.\mathrm{E}$$⇒\frac{1}{2}{\mathrm{Kx}}^{2}=\frac{1}{2}{\mathrm{mv}}^{2}$$⇒\mathrm{v}=\sqrt{\frac{\mathrm{K}}{\mathrm{m}}}\mathrm{x}$$=\sqrt{\frac{1}{2}}.4=2\sqrt{2}\text{\hspace{0.17em}}\mathrm{m}/\mathrm{s}$

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user
The passage contains a physics problem involving the Work Energy Theorem, where a sphere compresses a spring, and the velocity of the sphere is to be determined. The solution to the problem is provided, showing the calculation of the velocity.

TYPE: SINGLE_QUESTION_WITH_ANSWER