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Question
A railway train is travelling on a circular curve of 1500 metres radius at the rate of 66 km/hr. Through what angle has it turned in 10 seconds?
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Solution
Time = 10 seconds
Speed = \[66 km/h = \frac{66 \times 1000}{3600}m/s\]
We know:
\[\text{ Speed }= \frac{\text{ Distance }}{\text{ Time }}\]
\[ \Rightarrow \frac{66 \times 1000}{3600} = \frac{\text{ Distance }}{\text{ Time }}\]
\[ \Rightarrow\text{ Distance }= \frac{66 \times 1000}{3600} \times 10 = \frac{1100}{6} m\]
Now,
Radius of the curve = 1500 m
\[\therefore \theta = \frac{\text{ Arc }}{\text{Radius}}\]
\[ = \frac{\frac{1100}{6}}{1500}\]
\[ = \frac{1100}{1500 \times 6} = \frac{11}{90}\text{ radian}\]
So, the train will turn
\[\frac{11}{90}\] radian in 10 seconds.
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