Question

A solid cylinder of mass $250gm$ and radius $4cm$ is rolling down an inclined plane. The angle of inclination of the plane with horizontal is $\theta ={\sin }^{-1}\left(\frac{1}{10}\right).$ Total kinetic energy of the cylinder after 5 seconds would be :-

• A. $0.02$ joule
• B. $0.2$ joule
• C. $2.08$ joules
• D. $20$ joules

Answer 1

The correct option is C $2.08$ joules

$\begin{array}{c}\alpha =\frac{mg\sin \theta r}{\frac{3}{2}m{r}^2}=\frac{2g\sin \theta }{3r}=\frac{2\times 10\times \frac{1}{10}\times 100}{3\times 4}\\ =\frac{50}{3}rad/s^2\\ w=\alpha t=\frac{50\times 5}{3}rad/\sec .\\ K.E.=\frac{1}{2}\times \frac{3}{2}m{r}^2\cdot w^2\\ =\frac{3}{4}\times \frac{1}{4}\times {\left(\frac{4}{100}\right)}^2\cdot {\left(\frac{50\times 5}{3}\right)}^2\\ =\frac{50\times 50\times 5\times 5}{3\times 100\times 100}=\frac{25}{12}=2.08J.\\ Ans.\left(C\right)\end{array}$