Two blocks of masses ' $M$ ' and ' $m$ ' are placed on one another on a smooth horizontal surface as shown…

Two blocks of masses ' $M$ ' and ' $m$ ' are placed on one another on a smooth horizontal surface as shown in the figure.
The force ' $F$ ' is acting on the mass ' $M$ ' horizontally during time interval ' $t$ '. Assuming no relative sliding between the blocks, the work done by friction on the blocks is .......... .

1. $\frac{F t}{2(M+m)}$
2. $\frac{M+m}{m t^2}$
3. $\frac{m F^2 t^2}{2(M+m)^2}$
4. $\frac{F^2 t^2}{(M+m)}$

Solution

From (i) \& (ii), we get $a=\frac{F}{m+M}$ and $f=\frac{m F}{m+M}$ Distances moved in time $t(s)$ $ =\frac{1}{2} a t^2=\frac{1}{2}\left(\frac{F}{M+m}\right) t^2 $ Work done by friction $=f \times s$ $ =\left(\frac{m F}{M+m}\right) \times \frac{1}{2} \frac{F t^2}{(M+m)}=\frac{m F^2 t^2}{2(M+m)^2} $

Asked in: AP EAMCET 2017 (26 Apr Shift 1)

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