A flywheel of moment of inertia 9 × 103 kg m 2 is rotating with uniform angular speed of 5 rad s -1 If a torque of 9 × 104 Nm retard the wheel, then time in which the wheel comes to rest is

Question

A flywheel of moment of inertia 9 × 103 kg m 2 is rotating with uniform angular speed of 5 rad s -1 If a torque of 9 × 104 Nm retard the wheel, then time in which the wheel comes to rest is (A) 25 sec (B) 30 sec (C) 50 sec (D) 60 sec

Tardigrade Admin · Accepted Answer

As we know that, ω=ω0+α t ∴ (ω-ω0/t)=α ⇒ α=(0-5/t)=(-5/t) rad s-2 ∴ τ=I α ⇒ 9 × 104=9 × 103 × (5/t) ⇒ t=50 sec

Q. A flywheel of moment of inertia $9 \times 1 0^{3} k g m^{2}$ is rotating with uniform angular speed of $5 r a d s^{- 1}$ If a torque of $9 \times 1 0^{4}$ Nm retard the wheel, then time in which the wheel comes to rest is

$25 sec$

$30 sec$

$50 sec$

$60 sec$

As we know that, $ω = ω_{0} + α t$
$∴ \frac{ω - ω _{0}}{t} = α$
$\Rightarrow α = \frac{0 - 5}{t} = \frac{- 5}{t} r a d s^{- 2}$
$∴ τ = I α$
$\Rightarrow 9 \times 1 0^{4} = 9 \times 1 0^{3} \times \frac{5}{t}$
$\Rightarrow t = 50 sec$

Q. A flywheel of moment of inertia 9×103kgm2 is rotating with uniform angular speed of 5rads−1 If a torque of 9×104 Nm retard the wheel, then time in which the wheel comes to rest is

25sec

30sec

50sec

60sec