It d is the depth to which a bullet of kinetic energy K can penetrate into a human body of modulus of elasticity E. Then using the method of dimension establish a relation between d, K and E. If $$K=cdxEy$$, where c is a dimensionless constant. Modulus of elasticity $$=$$ Force Area ×lΔl (where$$ l is length and ∆l is change in $$length). The value of x $$+$$ y is $$_________$$

Question

It d is the depth to which a bullet of kinetic energy K can penetrate into a human body of modulus of elasticity E. Then using the method of dimension establish a relation between d, K and E. If $$K=cdxEy$$, where c is a dimensionless constant. Modulus of elasticity $$=$$ Force  Area ×lΔl  (where$$ l is length and ∆l is change in $$length). The value of x $$+$$ y is $$_________$$

Infinity Learn · Accepted Answer

$$ML2T$$−$$2=C$$[L]xML−$$1T$$−$$2y$$ On solving $$y=1$$ and $$x=3$$∴$$x+y=4$$

Dimensions of physical quantities

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$\begin{array}{l} [M L^{2} T^{- 2}] = C [L]^{x} {[M L^{- 1} T^{- 2}]}^{y} \\ On solving y = 1 and x = 3 \end{array}$
$∴ x + y = 4$

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Dimensions of physical quantities

Remember concepts with our Masterclasses.

ML2T−2=C[L]xML−1T−2y On solving y=1 and x=3∴x+y=4

Ready to Test Your Skills?

free study material

$\begin{array}{l} [M L^{2} T^{- 2}] = C [L]^{x} {[M L^{- 1} T^{- 2}]}^{y} \\ On solving y = 1 and x = 3 \end{array}$
$∴ x + y = 4$