A wheel having moment of inertia 2 kg-m2 about its vertical axis, rotates at the rate of 60 rpm about this axis. The torque which can stop the wheel's rotation in one minute would be

Question

A wheel having moment of inertia 2 kg-m2 about its vertical axis, rotates at the rate of 60 rpm about this axis. The torque which can stop the wheel's rotation in one minute would be (A) (2π/15) N-m (B) (π/12) N-m (C) (π/15) N-m (D) (π/18) N-m

Tardigrade Admin · Accepted Answer

Given, I=2 kg - m 2, ω0=(60/60) × 2 π rad / s ω=0, t=60 s The torque required to stop the wheel's rotation is τ=I α=I((ω0-ω/t)) ∴ τ=(2 × 2 π × 60/60 × 60) =(π/15) N - m

Q. A wheel having moment of inertia $2 k g - m^{2}$ about its vertical axis, rotates at the rate of $60$ rpm about this axis. The torque which can stop the wheel's rotation in one minute would be

$\frac{2 π}{15} N - m$

$\frac{π}{12} N - m$

$\frac{π}{15} N - m$

$\frac{π}{18} N - m$

Given, $I = 2 k g - m^{2}, ω_{0} = \frac{60}{60} \times 2 π r a d / s$
$ω = 0, t = 60 s$
The torque required to stop the wheel's rotation is
$τ = I α = I (\frac{ω _{0} - ω}{t})$
$∴ τ = \frac{2 \times 2 π \times 60}{60 \times 60}$
$= \frac{π}{15} N - m$

Q. A wheel having moment of inertia 2kg−m2 about its vertical axis, rotates at the rate of 60 rpm about this axis. The torque which can stop the wheel's rotation in one minute would be

152π​N−m

12π​N−m

15π​N−m

18π​N−m