AP EAPCET 07-Jul-2022 Shift 1 Paper

According to work-energy theorem, KE of stone = Elastic potential energy of rubber band.
Now, for rubber band;
Young's modulus =5×108N∕m2
Length, L=2×10−2m
Change of length, ∆L=2×10−2m
Area of cross-section, A=5×10−6m2
Elastic potential energy of rubber band
=

1

2

×Y×(strain)2×volume
=

1

2

×Y×(

∆L

L

)2×A×L
=

1

2

×5×108×(

2×10−2

2×10−2

)2×5×10−6×2×10−2
=25J
This energy is given to stone ( mass =20g);
⇒KE(stone)=E.P.E(Rubber‌band)
⇒

1

2

×mv2=25
⇒

1

2

×20×10−3×v2=25
⇒v2=

25×2

20×10−3

⇒v2=25×102
⇒v=5×10=50m∕ s