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Question

A catapult consists of two parallel rubber strings, each of length 10 cm and cross-sectional area 10 mm2 . When stretched by 5 cm, it can throw a stone of mass 100 gm to a vertical height of 25 m. Determine the Young's modulus of elasticity of rubber.

A
107 N/m2
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B
108 N/m2
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C
109 N/m2
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D
1010 N/m2
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Solution

The correct option is B 108 N/m2 Given, for the catapult L=10 cm,ΔL=5 cm,A=10 mm2 For the stone, m=100 gm,h=25 m A stretched catapult has elastic potential energy stored in it (Strain energy stored in both the rubber strings) U=2×(12×Stress×Strain×Volume) =2×(12×(Strain×Y)×Strain×Volume) ⇒U=2×(12×Y×(ΔLL)2×(A×L)) ⇒U=2×(12YA ΔL2L) This energy, when imparted to the stone, it flies off to a height 25 m. Energy possessed by the stone =mgh. Now, U=mgh ⇒YA ΔL2L=mgh ⇒Y=mgh LA ΔL2=(10−1 kg)×10 (m/s2)×(25 m)×(10×10−2 m)(10×10−6 m2)×(5×10−2 m)2 ∴Y=108 N/m2

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