AIIMS 2007
- Exam
- AIIMS
- Year
- 2007
- Subject
- Physics
- Chapter
- Rotational Motion
AIIMS 2007 · Physics · Rotational Motion
If a solid sphere of mass (1 ~kg ) and radius (0.1 ~m ) rolls...
If a solid sphere of mass (1 ) and radius (0.1 ) rolls without slipping at a uniform velocity of (1 / ) along a straight line on a horizontal floor, the kinetic energy is
Options
- A(\frac{7}{5} \mathrm{~J})
- B(\frac{2}{5} \mathrm{~J})
- C(\frac{7}{10} \mathrm{~J})
- D(1 \mathrm{~J})
Correct answer
C. (\frac{7}{10} \mathrm{~J})
Step-by-step solution
(\begin{gathered}
\mathrm{K} . \mathrm{E} \text{ of rolling }=\left(\frac{1}{2} m v^2+\frac{1}{2} I \cdot \frac{v^2}{R^2}\right) \\
\Rightarrow \mathrm{K} \cdot \mathrm{E}=\frac{1}{2} m v^2+\frac{1}{2} \cdot \frac{2}{5} \cdot \frac{m R^2 \cdot v^2}{R^2} \\
\mathrm{ K} . \mathrm{E}=\frac{1}{2} m v^2 \times \frac{7}{5} \\
m=1 \mathrm{ kg}, \quad v = 1 m/s \\
\mathrm{ K} \cdot \mathrm{E}=\frac{1}{2} \times 1 \times 1 \times \frac{7}{5}=\frac{7}{10} \mathrm{ J}
\end{gathered})