A stone of mass 20 , g is projected from a ru | vedclass

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(D) The elastic potential energy stored in the stretched rubber is given by $U = \frac{1}{2} k x^2$,where $k = \frac{YA}{L}$.Given:Mass $m = 20 \, g =

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(D) The elastic potential energy stored in the stretched rubber is given by $U = \frac{1}{2} k x^2$,where $k = \frac{YA}{L}$.Given:Mass $m = 20 \, g = 0.02 \, kg$Length $L = 0.1 \, m$Area $A = 10^{-6} \, m^2$Extension $x = 0.04 \, m$Young's modulus $Y = 0.5 	imes 10^9 \, N/m^2$By the law of conservation of energy,the elastic potential energy is converted into the kinetic energy of the stone:$\frac{1}{2} \left( \frac{YA}{L} ight) x^2 = \frac{1}{2} mv^2$Substituting the values:$\frac{0.5 	imes 10^9 	imes 10^{-6}}{0.1} 	imes (0.04)^2 = 0.02 	imes v^2$$\frac{500}{0.1} 	imes 0.0016 = 0.02 	imes v^2$$5000 	imes 0.0016 = 0.02 	imes v^2$$8 = 0.02 	imes v^2$$v^2 = \frac{8}{0.02} = 400$$v = 20 \, m/s$.

$A$ stone of mass $20 \, g$ is projected from a rubber catapult of length $0.1 \, m$ and area of cross-section $10^{-6} \, m^2$,stretched by an amount $0.04 \, m$. The velocity of the projected stone is $.... \, m/s$. (Young's modulus of rubber $= 0.5 \times 10^9 \, N/m^2$)

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