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An ice in the shape of cylinder is kept on a rough horizontal surface as shown in the figure. An initial velocity $v_{0}$ is imparted to cylindrical ice. The initial mass of ice is $m_{0}$ and coefficient of friction between ice and horizontal surface is ' $μ$ '. The initial temperature of ice $0^{0} C$ and its latent heat of fusion is $L$ . Choose the correct option(s).

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The velocity of cylindrical ice at time ‘ $t$ ’ is given by $(v_{0} + μ g t)$

The velocity of cylindrical ice at time ‘ $t$ ’ is given by $(v_{0} - μ g t)$

The mass of cylindrical ice at time ‘ $t$ ’ is given by $m_{0} e^{- \frac{μ g}{L} (v_{0} t - \frac{μ g t^{2}}{2})}$

The mass of cylindrical ice at time ‘ $t$ ’ is given by $m_{0} e^{- \frac{μ g}{L} (\frac{v_{0} t}{2} - \frac{μ g t^{2}}{2})}$

answer is B, C.

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