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JEE Main 202127 JulyMorning Shift
Exam
JEE Main
Year
2021
Date
27 July
Shift
Morning Shift
Subject
Physics
Chapter
Mechanical Properties of Solids

JEE Main 2021 · 27 July · Morning Shift · Physics · Mechanical Properties of Solids

A stone of mass 20g is projected from a rubber catapult of length 0...

A stone of mass 20g20g is projected from a rubber catapult of length 0.1m0 . 1m and area of cross section 10−6m2{10}^{- 6}{m}^{2} stretched by an amount 0.04m.0 . 04m . The velocity of the projected stone is ms−1.m{s}^{- 1} . (Young's modulus of rubber =0.5×109Nm−2= 0 . 5 \times {10}^{9}N{m}^{- 2})

Correct answer

20

Step-by-step solution

By energy conservation
12⋅YAL⋅x2=12mv2\dfrac{1}{2} \cdot \dfrac{YA}{L} \cdot {x}^{2} = \dfrac{1}{2}m{v}^{2}
0.5×109×10−6×(0.04)20.1=201000v2\dfrac{0 . 5 \times {10}^{9} \times {10}^{- 6} \times ( 0 . 04{)}^{2}}{0 . 1} = \dfrac{20}{1000}{v}^{2}
∴v2=400∴ {v}^{2} = 400
v=20ms−1v = 20m{s}^{- 1}
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