Q122 / 180 · KCET 2015 · Physics
The velocity - time graph for two bodies A and B are shown. Then the acceleration of A and B are in the ratio:
- A\(\tan 25^{\circ}\) to \(\tan 40^{\circ}\)
- Correct answerB\(\tan 25^{\circ}\) to \(\tan 50^{\circ}\)
- C\(\sin 25^{\circ}\) to \(\sin 50^{\circ}\)
- D\(\cos 25^{\circ}\) to \(\cos 50^{\circ}\)
Solution
Acceleration, \( a=\frac{d v}{d t} \)
\( \Rightarrow a= \) slope of velocity \( - \) time graph
Therefore, acceleration \( =\tan \theta \)
For body \( \mathrm{A}, a_{A}=\tan 25^{\circ} \)
For body \( \mathrm{B}, a_{B}=\tan 50^{\circ} \)
Therefore, ratio \( \frac{a_{A}}{a_{B}}=\frac{\tan 25^{\circ}}{\tan 50^{\circ}} \)
\( \Rightarrow a= \) slope of velocity \( - \) time graph
Therefore, acceleration \( =\tan \theta \)
For body \( \mathrm{A}, a_{A}=\tan 25^{\circ} \)
For body \( \mathrm{B}, a_{B}=\tan 50^{\circ} \)
Therefore, ratio \( \frac{a_{A}}{a_{B}}=\frac{\tan 25^{\circ}}{\tan 50^{\circ}} \)
Hence, the correct answer is option: 'B'.