An ice cube of mass `M_(0)` is given a velocity `v_(0)` on a round horizontal surface with coefficient of friction `mu`. The block is at its melting point and latent heat of fusion of ice is `L` . The block receive heat only due to the friction forces and all work is converted into heat. Find the mass of the remaining ice block after time t.

Options

A. `m=m_(0)e^(-(2mug)/(L)(V_(0)t+(1)/(2)mu"gt"^(2)))`
B. `m=m_(0)e^(-(2mu)/(L)(V_(0)t-(1)/(2)mu"gt"^(2)))`
C. `m=m_(0)e^(-(3mu)/(L)(V_(0)t-(1)/(2)mu"gt"^(2)))`
D. `m=m_(0)e^(-(2mu)/(L)(V_(0)t-mu"gt"^(2)))`

Answer

B

Explanation

`mu mg v =-((dm)/(dt))L`
`implies underset(m_(0))overset(m)(int) (dum)/(m)=-(mug)/(L) underset(0)overset(t)(int)(mu"gt")dt`
`implies m=m_(0)e^(-(mug)/(L)(v_(0)t-(1)/(2)mu"gt"^(2))`