Question

A cart of total mass $50\text{kg}$ is at rest on a horizontal road having coefficient of friction 0.1. Gases are ejected from this cart backwards with velocity $20\text{m/s}$ w.r.t the cart. The rate of ejection of gases is $2\text{kg/s}$. The cart will start moving after time $t=$ (seconds) [Take $g=10{\text{m/s}}^2$]

Answer 1

Given,
Mass of cart $\left(m_0\right)=50\text{kg}$
Relative velocity of gas ejected $\left(v_r\right)=20\text{m/s}$
Cart will start moving when the thrust force due to the gas overcomes the limiting force of friction.
i.e $\mu mg=v_r\left(\frac{-dm}{dt}\right)$
Here, mass at time $t,m=50-2t$
$\Rightarrow 0.1\times (50-2t)\times 10=20\times 2$
$\Rightarrow t=5\text{s}$