Question

It is found that the force required to row a boat in a river is proportional to the speed of the boat. When the speed of the boat is kept $v\text{km / hr}$, the power expended by the boat engine is 24 horse power. What shall be the power required, if one wishes to row the boat at a speed $2v\text{km/hr}$?

• A. $48\text{hp}$
• B. $96\text{hp}$
• C. $144\text{hp}$
• D. $192\text{hp}$

Answer 1

The correct option is B $96\text{hp}$

Let $F=kv$
Now, $P=F.v=k{v}^2$
$\frac{P^{\prime }}{P}=\frac{k4v^2}{k{v}^2}=4$
$P^{\prime }=4P=4\times 24=96\text{hp}$
Hence, the correct option is (B).