AP EAPCET 06-Jul-2022 Shift 1 Paper

Given, f1=300‌rpm=‌

300

60

‌rps=50‌Hz
f2=0
(As fan is switched off)
⇒‌‌t=80 s
Constant angular deceleration =α(α<0). By 2nd kinematical equation
θ=ω1t+‌

1

2

αt2
2πn=(2πf1)t+‌

1

2

αt2 ...... (i) [∵ω1=2πf1]
By lst kinematical equation,
α=‌

ω2−ω1

t

=‌

2π(f2−f1)

t

‌=‌

2π(0−50)

80

=‌

−5π

4

‌rad∕ s2
⇒α‌=‌

−5π

4

‌rad∕ s2
Now, putting the value of α in Eq. (i), we get,
2πn‌={(2π×50)×80}+‌

1

2

{‌

−5π

4

×802}
⇒n‌=(‌

8000π−5π×800

2π

)
‌=‌

8000π−4000π

2π

=‌

4000π

2π

n‌=200