First slide

Elastic behaviour of solids

Question

A rubber cord catapult has cross-sectional area 25 mm² and initial length of rubber cord is 10 cm. It is stretched to 5 cm and then released to project a missile of mass 5 gm. Taking $Y_{rubber} = 5 \times 10^{8} N / m^{2}$ , velocity of projected missile is

Easy

A

20 $m s^{- 1}$
B

100 $m s^{- 1}$
C

250 $m s^{- 1}$
D

200 $m s^{- 1}$

Solution

Potential energy stored in the rubber cord catapult will be converted into kinetic energy of mass.
$\begin{array}{l} \begin{array}{l} \frac{1}{2} m v^{2} = \frac{1}{2} \frac{Y A l^{2}}{L} \\ \Rightarrow v = \sqrt{\frac{Y A l^{2}}{m L}} \end{array} \\ \Rightarrow v = \sqrt{\frac{5 \times 10^{8} \times 25 \times 10^{- 6} \times {(5 \times 10^{- 2})}^{2}}{5 \times 10^{- 3} \times 10 \times 10^{- 2}}} = 250 m / s \end{array}$

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