| A mass of 0.5 kg moving with a speed of 1.5 m/son a horizontal smooth surface, collides with a nearly weightless spring of force constant \[k=50\text{ }N/m\]. The maximum compression of the spring would be:[AIPMT (S) 2004] |
 |
A) 0.15 m
B) 0.12 m
C) 1.5 m
D) 0.5 m
Correct Answer: A
Solution :
| Key Idea: The kinetic energy of mass must be converted into energy stored in spring at the time mass strikes the spring. |
| By the law of conservation of energy, kinetic energy of mass = energy stored in spring |
| i.e., \[\frac{1}{2}m{{v}^{2}}=\frac{1}{2}k{{x}^{2}}\] |
| \[\therefore \] \[{{x}^{2}}=\frac{mv}{k}\] |
| \[\Rightarrow \] \[x=\sqrt{\left( \frac{m{{v}^{2}}}{k} \right)}\] |
| \[\Rightarrow \] \[x=\sqrt{\left( \frac{0.5\times 1.5\times 1.5}{50} \right)}\] |
| \[\therefore \] \[=0.15\,m\] |
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