Question

A bullet of mass 10 g moving with a speed of `20 m//s` hits an ice block of mass 990 g kept on a frictionless floor and gets stuck in it. How much ice will melt if `50%` of the lost kinetic energy goes to ice?
(Temperature of ice block `= 0^@C`.)

Answer 1

Correct Answer - C
Velocity of bullet + ice block,
`V = ((10g)xx(20 m//s))/1000 g = 0.2 m//s`
Loss of KE `= 1/2 mv^2 - 1/2 (m+M)V^2`
`= 1/2 [0.01 xx (20)^2 - 1 xx (0.2)^2]`
`=1/2 [4- 0.04] = 1.98 J`
`:.` Heat received by ice block `= (1.98)/(4.2 xx2) cal `
`= 0.24 cal`
`:.` Mass of ice melted `= (0.24cal)/(80 cal//g)`
`=0.003 g` .