A hunter fired a metallic bullet of mass 'm' kg from a gun towards an obstacle and it just melts when it is stopped by the obstacle. The initial temperature of the bullet is `300K`. If `(1^(th))/(4)` of heat is absorbed by the obstacle, then the minimum velocity of the bullet is
[Melting point of bullet =600K,
Specific heat of bullet `=0.3 "cal g"^(-1).^(0)C^(-1)`,
Latent heat of fusion of bullet `=6 cal g^(-1)`].

Options

A. `410ms^(-1)`
B. `260ms^(-1)`
C. `460ms^(-1)`
D. `310ms^(-1)`

Answer

A

Explanation

Metallic bullet mass = mkg
Intial bullet temperature =300k.
`(1^th)/(4)` heat absorbed by obstacle total heat =1 .
remaining heat `=1-(1)/(4)=(3)/(4)`. Bullet melting point =60k.
Bullet specific heat `=0.03 cal g^(-1) .^(@)C^(-1)`.
Bullet latent heat fusion `=6cal g^(-1)`.
`(3)/(4)((1)/(2)mr^2)=ms Delta theta +ml` .
`delta[(3)/(4)v^2=0.03xx4200 xx 300 +6xx 4200]delta`
`v^2==(8)/(3)[0.01xx4200 xx 300 +2 xx 4200]`
`v^2=sqrt(168000)`
`v=410m//s`.