Moment of inertia of a body about an axis is 4 kg - m 2. The body is initially at rest and a torque of 8 N-m starts acting on it along the same axis. Work done by the torque in 20 s, in joules, is

Question

Moment of inertia of a body about an axis is 4 kg - m 2. The body is initially at rest and a torque of 8 N-m starts acting on it along the same axis. Work done by the torque in 20 s, in joules, is (A) 40 (B) 640 (C) 2560 (D) 3200

Tardigrade Admin · Accepted Answer

Given, l=4 kg - m 2, τ=8 N - m and t=20 s τ=l α ⇒ α=(τ/l)=(8/4)=2 θ=(1/2) α t2 ⇒ θ=(1/2) × 2 × 20 × 20=400 ω=τ θ=8 × 400=3200 J

Q. Moment of inertia of a body about an axis is $4 k g - m^{2}$ . The body is initially at rest and a torque of $8 N - m$ starts acting on it along the same axis. Work done by the torque in $20 s$ , in joules, is

40

640

2560

3200

Given, $l = 4 k g - m^{2}, τ = 8 N - m$ and $t = 20 s$
$τ = l α$
$\Rightarrow α = \frac{τ}{l} = \frac{8}{4} = 2$
$θ = \frac{1}{2} α t^{2}$
$\Rightarrow θ = \frac{1}{2} \times 2 \times 20 \times 20 = 400$
$ω = τ θ = 8 \times 400 = 3200 J$

Q. Moment of inertia of a body about an axis is 4kg−m2. The body is initially at rest and a torque of 8N−m starts acting on it along the same axis. Work done by the torque in 20s, in joules, is

40

640

2560

3200

Given, l=4kg−m2,τ=8N−m and t=20s τ=lα ⇒α=lτ​=48​=2 θ=21​αt2 ⇒θ=21​×2×20×20=400 ω=τθ=8×400=3200J

Q. Moment of inertia of a body about an axis is $4 k g - m^{2}$ . The body is initially at rest and a torque of $8 N - m$ starts acting on it along the same axis. Work done by the torque in $20 s$ , in joules, is

Given, $l = 4 k g - m^{2}, τ = 8 N - m$ and $t = 20 s$
$τ = l α$
$\Rightarrow α = \frac{τ}{l} = \frac{8}{4} = 2$
$θ = \frac{1}{2} α t^{2}$
$\Rightarrow θ = \frac{1}{2} \times 2 \times 20 \times 20 = 400$
$ω = τ θ = 8 \times 400 = 3200 J$