Q. A truck is moving on a frictionless surface with uniform velocity of ${10\ ms}^{- 1}$. A leak occurs in the water tank of the truck at the rate of ${2\ kgs}^{- 1}.$ What is the speed of truck after 50 s if the mass of truck is 100 kg and mass of water in truck initially was 100 kg?
A) ${20\ ms}^{- 1}$
B) ${10\ ms}^{- 1}$
C) ${5\ ms}^{- 1}$
D) None of these
Explanation
(d) $Given\ that,\ u = {10\ ms}^{- 1},\frac{dm}{dt} = 2\ {kgs}^{- 1}$
Total mass of the truck, $M = (100 + 100)\ kg = 200\ kg$
We know that,
$F = \frac{u\ dm}{dt}$
$or\ \ F = 10 \times 2 = 20\ N$
$or\ Ma = 20\ N$
$or\ \ 200a = 20\ N$
$or\ \ a = \frac{20}{200}ms^{- 2} = \frac{1}{10}ms^{- 2}$
now, we know that,
$a = \frac{v - u}{t}\ \ \ (u = 10ms^{- 2},\ t = 50s)$
$\Longrightarrow \ \ \frac{1}{10} = \frac{v - 10}{50} \Longrightarrow v = {15\ ms}^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.