Question

A truck is moving on a frictionless surface with uniform velocity of 10 $m{s}^{-1}$/. A leak occurs in the water tank of the truck at the rate of 2 $kg{s}^{-1}$. What is the speed of truck after 50 s if the mass of truck is 100 kg and mass of water in the truck initially was 100 kg?

• A. 20 $m{s}^{-1}$
• B. 10 $m{s}^{-1}$
• C. 5 $m{s}^{-1}$
• D. none of these

Answer 1

The correct option is A 20 $m{s}^{-1}$

$Given:$ velocity$=10$ $m{s}^{-1}$ ; Rate $=2Kg{s}^{-1}$

$Solution:$ Mass of system $=100+100$

$=200kg$

Water leaks at rate $2kg/s$

So after $50sec$

$m=50\times 2$

$=100kg$

So,final mass $=200-100$

$=100kg$

Initial momentum $=$ Final momentum

$m_1{u}_1=m_2{u}_2$

$u_2=\frac{m_1}{m_2}{u}_1$

$=\frac{200\times 10}{100}$

$=20m{s}^{-1}$

$So,the$ $correct$ $option:A$