Question

if the depth d to which a bullet of kinetic energy K can penetrate into a human body of elasticity E, using the method of dimensions, establish a relation between d,K and E.​ agar kisi ne faltu ka ans diya to vo____

Answer 1

dimension of depth, d = [L]

dimension of Kinetic energy , K = [ML²T-²]

dimension of elasticity , E = [ML-¹T-²]

now from dimensional analysis

E = C d^x K^y , where C is proportionality constant.

putting dimensions of E, d and K.

[ML-¹T-²] = C[L]^x [ML²T-²]^y

or, [ML-¹T-²] = C[M]^y [L^(x + 2y)] [T^(-2y)]

on comparing we get,

y = 1,

x + 2y = -1 => x = -3

-2y = -2 => y = 1

so, x = -3 and y = 1

hence, relation between d, K and E is E = Cd^-3K or, C (K/d³)

we can say that elasticity, E is directly proportional to (K/d³)