MHT CET · Physics · Work Power Energy
A sphere of mass 25 gram is placed on a vertical spring. Spring is compressed by \(0.2 \mathrm{~m}\) using a force \(5 \mathrm{~N}\). When the spring is relaxed, mass is reaching a height of \(\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right)\)
- A \(6 \mathrm{~cm}\)
- B \(8 \mathrm{~cm}\)
- C \(10 \mathrm{~cm}\)
- D \(2 \mathrm{~m}\)
Answer & Solution
Correct Answer
(D) \(2 \mathrm{~m}\)
Step-by-step Solution
Detailed explanation
Gravitational potential energy gained by the ball \(=\) Elastic potential energy in the spring
\(\begin{aligned} & \mathrm{mgh}=\frac{1}{2} \mathrm{Fx} \\ & \therefore \mathrm{h}=\frac{\mathrm{Fx}}{2 \mathrm{mg}} \\ & =\frac{5 \times 0.2}{2 \times 25 \times 10^{-3} \times 10} \\ & =2 \mathrm{~m} \end{aligned}\)
\(\begin{aligned} & \mathrm{mgh}=\frac{1}{2} \mathrm{Fx} \\ & \therefore \mathrm{h}=\frac{\mathrm{Fx}}{2 \mathrm{mg}} \\ & =\frac{5 \times 0.2}{2 \times 25 \times 10^{-3} \times 10} \\ & =2 \mathrm{~m} \end{aligned}\)
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