A lead bullet moving with velocity ' v ' strikes a wall and stops. 75% of its energy is converted into heat. If the increase in the temperature is n J s v 2 , then the value of n is { s =

Question

A lead bullet moving with velocity ' v ' strikes a wall and stops. 75% of its energy is converted into heat. If the increase in the temperature is n J s v 2 ​ , then the value of n is { s = specific heat of lead , J = mechanical equivalent of heat }

TestHub · Accepted Answer

The initial kinetic energy of the bullet is $K = \frac{1}{2} m v^{2}$ .

The energy converted into heat is $W = 75% of K = \frac{3}{4} \times \frac{1}{2} m v^{2} = \frac{3}{8} m v^{2}$ .

Using the relation $W = J H$ , where the heat absorbed by the bullet is $H = m s Δ T$ :

$\frac{3}{8} m v^{2} = J m s Δ T$

$Δ T = \frac{3 v ^{2}}{8 J s} = \frac{v ^{2}}{( \frac{8}{3} ) J s}$

Comparing this with the given expression $Δ T = \frac{v ^{2}}{n J s}$ , we get:

$n = \frac{8}{3}$

Answer: $\frac{8}{3}$

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