Physics - NLM Question with Solution | TestHub

Mass of the cart with sand changes then its acceleration also changes. $a=\frac{F}{m}=\frac{F}{m_0-\mu t}$ where $m$ is mass of system at time $t$, $\begin{array}{rl}& m=m_0-\mu t\\ & a=\frac{F}{m_0-\mu t}\text{ or }\frac{dv}{dt}=\frac{F}{m_0-\mu t}\end{array}$ $\begin{array}{rl}& {\int }_0^{v}dv=F{\int }_0^t\frac{dt}{m_0-\mu t}\\ & v=\frac{F}{\mu }\ln \left(\frac{m_0}{m_0-\mu t}\right)\end{array}$ Here $F=10\mathrm{N};\mu =0.5\mathrm{kg}/\mathrm{s}$ $m_0=2$ metric tone $m_0-\mu t=1$ metric tone $\therefore v=\frac{10}{0.5}\ln (2)=20\times 0.693=13.86\mathrm{m}/\mathrm{s}$