Question

If the ground is smooth, what is the total kinetic energy of body at $t=2s$. Initially, the body was at rest.

• A. $25J$
• B. $16.67J$
• C. $50J$
• D. $37.5J$

Answer 1

The correct option is C $50J$

${\tau }_o=I_O\alpha$

$F\left(2R\right)-FR=I\alpha ⟹FR=I\alpha$

$10\times 1=4\alpha$ gives $\alpha =2.5rad/s^2$

Now $w=w_i+\alpha \left(t\right)$

$w=0+2.5\left(2\right)=5rad/s$

$K.E=\frac{1}{2}I{w}^2=\frac{1}{2}\times 4(5{)}^2$

$K.E=50J$