Question

The train is moving on a circular of radius 1500m at the rate of 66km per hour. Through what angle has it turned in 10seconds
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Answer 1

Step-by-step explanation:

Correct option is B)

Radius of circular curve, R=1500m

Speed of trains, S=66 km/hr

Sonverting speed of train into m/sec

Speed of train =66×

18

5

=

3

110

m/s

Time travelled, t=10 sec

Distance converted, d=s×t

=

3

110

×10=

3

1100

m

circumference of circular curve, C=2πR

=2×

7

22

×1500

=

7

66000

m

As d<c, revolutions completed =0

Angles turned , θ=

c

d

×2π radians

=

(66000/7)

(1100/3)

×2×

7

22

=

180

44

radians

=

45

11

radians

Angle turned =

45

11

radians

Answer 2

Given:

• Radius of circular curve, R=1500m
• Speed of trains, S=66 km/hr

Solution:

Converting speed of train into m/sec:

Speed of the train = $66 \times \frac{5}{18} \times \frac{110}{3}$

Time travelled, t = 10 sec

Distance covered, d = s × t

= $\frac{110 }{3} \times 10$

= $\frac{1100}{3}$

Circumference of the circular curve = 2πr

= $2 \times \frac{22}{7} \times 1500$

$\frac{66000}{7}$

As d > c, revolutions completed = 0

Angles turned, θ = $\frac{d}{c} \times 2πr \: radius$

$\frac{44}{180} \: radians$

$\frac{11}{15} \: radians$

Hence, the angles turned are 11/15 radians.

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