Exam

JIPMER

Year

2011

Subject

Physics

Chapter

Work, Power and Energy

JIPMER 2011 · Physics · Work, Power and Energy

A ball of mass 2 kg moving with velocity 3 ~m / s , collides with...

A ball of mass 2 kg moving with velocity $3 \mathrm{~m} / \mathrm{s}$, collides with spring of natural length 2 m and force constant $144 \mathrm{~N} / \mathrm{m}$. What will be length of compressed spring?

Step-by-step solution

Let spring is compressed by a length $x$. Kinetic energy of ball = Potential energy of spring $i e, \quad \frac{1}{2} m v^2=\frac{1}{2} k x^2$ Given, $\quad m=2 \mathrm{~kg}, v=3 \mathrm{~m} / \mathrm{s}, k=144 \mathrm{~N} / \mathrm{m}$ $\therefore \quad \frac{1}{2} \times 2 \times(3)^2=\frac{1}{2} \times 144 \times x^2$ $\therefore \quad x=\sqrt{\frac{9}{72}}=\frac{1}{2 \sqrt{2}} \mathrm{~m}$ Hence, length of compressed spring $=2-\frac{1}{2 \sqrt{2}}$ $=\frac{4 \sqrt{2}-1}{2 \sqrt{2}}$ $=1.5 \mathrm{~m}$