Question

A flywheel rotates about an axis. Due to friction at the axis,
it experiences an angular retardation proportional to its
angular velocity. If its angular velocity falls to half while it
makes n rotations, how many more rotations will it make
before coming to rest?
(a) 2n (b) n
(c) n/2 (d) n/3

Answer 1

Answer:

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Explanation:

α is propotional to ω

Let α=kω (∵k is a constant)

dt

dω

=kω[also

dt

dθ

=ω⇒dt=

ω

dθ

]

∴

dθ

ωdω

=kω⇒dω=kdθ

Now ∫

ω

ω/2

dω=k∫dθ

∫

ω/2

0

dω=k∫

0

θ

dθ⇒−

2

ω

=kθ⇒−

2

ω

=kθ

1

(∵θ

1

=2πn)

∴θ=θ

1

or 2πn

1

=2πn

n

1

=n

Answer 2

Explanation:

bob m. The bob

is given a charge q. The pendulum is suspended between

the vertical plates of the charged parallel plate capacitor. If

E is the field strength between the plates, then time period

T equal to

(a) 2π √????/g (b) 2π √????/g + qE/m

(c) 2π √????/g - qE/m

(d) 2π √????/√g² + (qE/m)²