question_answer

A truck can move up a road having the grade of 1 m rise for every 50 m with a speed of 15 km/hr. The resisting force is equal to \[\frac{1}{25}\] th the weight Au of the truck. How fast will the same truck move down the hill with the same horse power?

A)  30 km/hr            

B)  45 km/hr  

C)  60km7hr       

D)         75 km/hr

Correct Answer: B

Solution :

 Referring figures,\[\sin \theta =\frac{1}{50}\]                 \[P={{F}_{1}}{{v}_{1}}={{F}_{2}}{{v}_{2}}=\]same                              ? (i) For upward motion of truck,                 \[{{F}_{1}}=\frac{Mg}{25}+mg\sin \theta \]                 \[=\frac{Mg}{25}+\frac{Mg}{50}=\frac{3}{50}Mg\]                           ? (ii) For downward motion of truck,         \[{{F}_{2}}=\frac{Mg}{25}-\frac{Mg}{50}=\frac{Mg}{50}\]                     ? (iii) Using equation (ii) and (m) in equation (i), we have                 \[\frac{3}{50}Mg{{v}_{1}}=\frac{Mg}{50}{{v}_{2}}\] \[\Rightarrow \]                         \[{{v}_{2}}=3{{v}_{1}}\] \[\therefore \]Downward speed of the truck                  \[=3\times 15=\mathbf{45}\,\,\mathbf{km/hr}\]