Question

A truck of mass $30,000kg$ moves up an inclined plane of slope $1$ in $\sqrt{3}$ at a speed of $6kmph$. The power of the truck is (given $g=10m{s}^{-2}$)

• A. $250kW$
• B. $10kW$
• C. $5kW$
• D. $2.5kW$

Answer 1

The correct option is A $250kW$

Given,

Mass of truck, $M=30000kg$

Slope of incline, $\tan \theta =\frac{1}{\sqrt{3}}\Rightarrow \theta ={30}^o$

Velocity, $v=6kmph=6\times \frac{5}{18}=\frac{5}{3}m{s}^{-1}$

Power,

$P=weight\times upwardvelocity=mg.\left(v\sin {30}^o\right)$

$P=3\times {10}^4\times 10\times \frac{5}{3}\times \frac{1}{2}=250kW$

Hence, Power of truck is $250kW$