A) \[{{10}^{-3}}\]
B) \[1.5\times {{10}^{-3}}\]
C) \[2\times {{10}^{-3}}\]
D) \[2.5\times {{10}^{-3}}\]
Correct Answer: A
Solution :
Initial mass of ice block m = 42kg Initial velocity of ice block \[u=4\,m{{s}^{-1}}\] Final velocity of ice block v =0 Let retardation = a Using IIIrd equation of motion, we get \[{{v}^{2}}-{{u}^{2}}-2as\] (\[-ve\]sign is taken for retardation) \[2as={{u}^{2}}-{{v}^{2}}\] \[as=\frac{{{u}^{2}}-{{v}^{2}}}{2}=\frac{{{(4)}^{2}}-{{(0)}^{2}}}{2}\] \[as=8{{m}^{2}}/{{s}^{2}}\] Heat generated = work done against friction \[Q=F\times s\] \[Q=m\times a\times s\] \[Q=42\times 8\] \[Q=336\,J\] Due to this heat, let M kg of ice melts. So, Q = ML \[\Rightarrow \] \[M=\frac{Q}{L}=\frac{336}{3.36\times {{10}^{5}}}kg\] \[M=1\times {{10}^{-3}}\,kg\]
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