Question

A uniform solid sphere of mass 200 gm rolls without slipping on a plane surface so that its center moves at a speed of 2.00 cm/sec. Its kinetic energy is :

• A. $5.6\times {10}^{-5}J$
• B. $5.6\times {10}^{-4}J$
• C. $5.6\times {10}^{-3}J$
• D. $5.6\times {10}^{-2}J$

Answer 1

Answer: (A)

$5.6\times {10}^{-5}J$

$\begin{array}{cc}\text{Given-}& \ast \text{mass of Sphere}=200gm=0.2kg\left(m\right)\\ \ast & \text{velocity}\left(v\right)=2cm/s=0.02m/s\end{array}$

$\begin{array}{c}\text{Kinetic Energy of Sphere (KE)}\\ \begin{array}{c}K{E}_{\text{Total}}=KE\text{rranslation}+KE\text{Rotational}\\ K{E}_T=\frac{1}{2}m{v}^2+\frac{1}{2}I{\omega }^2\\ \text{We Rnow that moment of Inertiaof sphere}\\ I=\frac{2}{5}m{R}^2\end{array}\end{array}$

$\begin{array}{c}\Rightarrow k{E}_T=\frac{1}{2}m{v}^2+\frac{1}{5}m{\omega }^2{R}^2=\frac{7}{10}m{v}^2\because (v=R\omega )\\ \Rightarrow k{E}_T=\frac{7}{10}\times 0.2\times (0.02{)}^{2}J\\ =5.6\times {10}^{-5}J\\ \text{Hence, option}\left(A\right)\text{is the correct option.}\end{array}$