Question

An electric motor exerts a constant torque $10\text{N-m}$ on a grind stone mounted on a shaft. MOI of the grind stone about the shaft is $2{\text{kg m}}^2$. If the system starts from rest find the work done in $8\text{s}$.

• A. $1600\text{J}$
• B. $1200\text{J}$
• C. $800\text{J}$
• D. $600\text{J}$

Answer 1

The correct option is A $1600\text{J}$

We know that the relation between torque $\left(\tau \right)$ and the angular acceleration $\left(\alpha \right)$ is,

$\alpha =\frac{\tau }{I}=\frac{10}{2}=5{\text{rad/s}}^2$

Also by the rotational equation of motion,
$($As starting from rest ${\omega }_0=0)$.

$\omega ={\omega }_0+\alpha t=5\left(8\right)=40{\text{rad s}}^{-1}$

From the Work-Energy theorem , work done$\left(W\right)$ is equal to change in Kinetic energy$(K.E)$,

$W=\Delta KE=\frac{1}{2}I{\omega }^2-0=\frac{1}{2}\times 2\times (40{)}^2=1600\text{J}$

Hence option A is the correct answer.