9th Class
Science
Work and energy
Question Bank
Work, Energy and Power
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 \[=3\times 15=\mathbf{45}\,\,\mathbf{km/hr}\]