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`.)
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Velocity of bullet + ice blocmk `V=((10gm)xx(20m//s))/(1000gm)=0.2m//s` Loss of K.E. `=1/2 mv^(2) - 1/2 (m+M)V^(2)` `=1/2[0.01xx(20)^(2)-1xx(0.2)^(2)]=1.98J` `:.` Heat generated `=1.98/4.2` cal `:.` Heat received by ice block `=1.98/(4.2xx2)` cal `=0.24` cal `:.` Mass is ice melted `=((0.24"cal"))/((80"cal"//gm))=0.003 gm`
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