A grindstone has a moment of inertia of 10 kgm 2. A constant torque is applied and the grindstone is found to have a speed of 200 rpm. 20 sec, after starting from rest, what will be the torque?

Question

A grindstone has a moment of inertia of 10 kgm 2. A constant torque is applied and the grindstone is found to have a speed of 200 rpm. 20 sec, after starting from rest, what will be the torque? (A) 2.14 Ns (B) 6 Ns (C) 4 Ns (D) 3.33 π Ns

Tardigrade Admin · Accepted Answer

ω0=0 ω=2 π n=2 × π × (200/60) =(20 π/3) rad / sec angular acceleration α=(ω-ω0/t) =((20 π/3)-0/20) =(20 π/3 × 20) =(π/3) rad / s 2 ∴ τ=I α=10 × (π/3) =3.33 π Ns

Q. A grindstone has a moment of inertia of $10 k g m^{2}$ . A constant torque is applied and the grindstone is found to have a speed of 200 rpm. 20 sec, after starting from rest, what will be the torque?

$2.14 N s$

$6 N s$

$4 N s$

$3.33 π N s$

$ω_{0} = 0 ω = 2 πn = 2 \times π \times \frac{200}{60}$
$= \frac{20 π}{3} r a d / sec$
angular acceleration $α = \frac{ω - ω _{0}}{t}$
$= \frac{\frac{20 π}{3} - 0}{20}$
$= \frac{20 π}{3 \times 20}$
$= \frac{π}{3} r a d / s^{2}$
$∴ τ = I α = 10 \times \frac{π}{3}$
$= 3.33 π N s$

Q. A grindstone has a moment of inertia of 10kgm2. A constant torque is applied and the grindstone is found to have a speed of 200 rpm. 20 sec, after starting from rest, what will be the torque?

2.14Ns

6Ns

4Ns

3.33πNs