A thin rod of mass m and length 2L is made to rotate about an axis passing through its centre and perpendicular to it. If its angular velocity changes from 0 to ω in time t, the torque acting on it is

Question

A thin rod of mass m and length 2L is made to rotate about an axis passing through its centre and perpendicular to it. If its angular velocity changes from 0 to ω in time t, the torque acting on it is (A) ( m ℓ2 ω/12 t ) (B) ( m ℓ2 ω/3 t ) (C) ( m ℓ2 ω/ t ) (D) (4 m ℓ2 ω/3 t )

Tardigrade Admin · Accepted Answer

Since, τ=I α So, τ=(( m (2 ℓ)2/12))((ω/ t )) or τ=( m × 4 ℓ2 × ω/12 × t ) Or τ=(4 m ℓ2 ω/12 t)=((m ℓ2 ω/3 t))

Q. A thin rod of mass $m$ and length $2 L$ is made to rotate about an axis passing through its centre and perpendicular to it. If its angular velocity changes from 0 to $ω$ in time $t,$ the torque acting on it is

$\frac{m ℓ ^{2} ω}{12 t}$

$\frac{m ℓ ^{2} ω}{3 t}$

$\frac{m ℓ ^{2} ω}{t}$

$\frac{4 m ℓ ^{2} ω}{3 t}$

Since, $τ = I α$
So, $τ = (\frac{m ( 2 ℓ ) ^{2}}{12}) (\frac{ω}{t})$
or $τ = \frac{m \times 4 ℓ ^{2} \times ω}{12 \times t}$
Or $τ = \frac{4 m ℓ ^{2} ω}{12 t} = (\frac{m ℓ ^{2} ω}{3 t})$

Q. A thin rod of mass m and length 2L is made to rotate about an axis passing through its centre and perpendicular to it. If its angular velocity changes from 0 to ω in time t, the torque acting on it is

12tmℓ2ω​

3tmℓ2ω​

tmℓ2ω​

3t4mℓ2ω​