A wheel of radius 0.4 m can rotate freely about its axis as shown in the figure. A string is wrapped over its rim and a mass of 4 kg is hung. An angular acceleration of 8 rad - s -2 is produced in it due to the torque. Then, moment of inertia of the wheel is (g=10 ms -2. )

Question

A wheel of radius 0.4 m can rotate freely about its axis as shown in the figure. A string is wrapped over its rim and a mass of 4 kg is hung. An angular acceleration of 8 rad - s -2 is produced in it due to the torque. Then, moment of inertia of the wheel is (g=10 ms -2. ) (A) 2 kg - m 2 (B) 1 kg - m 2 (C) 4 kg - m 2 (D) 8 kg - m 2

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/658ceefa67037ce4766c1e3b2f331d10-.png" /> Given, r=0.4 m, α=8 rad s -1 m=4 kg , I=? Torque, τ=I α m g r=I ⋅ α or 4 × 10 × 0.4=I × 8 ⇒ I=(16/8)=2 kg - m 2 or I=2 kg - m 2

Q. A wheel of radius $0.4 m$ can rotate freely about its axis as shown in the figure. A string is wrapped over its rim and a mass of $4 k g$ is hung. An angular acceleration of $8 r a d - s^{- 2}$ is produced in it due to the torque. Then, moment of inertia of the wheel is $(g = 10 m s^{- 2}$ )

$2 k g - m^{2}$

$1 k g - m^{2}$

$4 k g - m^{2}$

$8 k g - m^{2}$

Given, $r = 0.4 m$ ,
$α = 8 r a d s^{- 1}$
$m = 4 k g, I = ?$
Torque, $τ = I α$
$m g r = I \cdot α$
or $4 \times 10 \times 0.4 = I \times 8$
$\Rightarrow I = \frac{16}{8} = 2 k g - m^{2}$
or $I = 2 k g - m^{2}$

Q. A wheel of radius 0.4m can rotate freely about its axis as shown in the figure. A string is wrapped over its rim and a mass of 4kg is hung. An angular acceleration of 8rad−s−2 is produced in it due to the torque. Then, moment of inertia of the wheel is (g=10ms−2 )

2kg−m2

1kg−m2

4kg−m2

8kg−m2