Question

If a body moving in a circle of radius $10m$ is covering a displacement of $20m$, in $10s$, then the speed of the body can be

• A. $n\pi$, where $n=1,3,\mathrm{5.....}$
• B. $n\pi$, where $n=1,2,3,....$
• C. $\frac{n\pi }{2}$, where $n=1,3,\mathrm{5....}$
• D. $\frac{n\pi }{2}$, where $n=1,2,\mathrm{3....}$

Answer 1

The correct option is A $n\pi$, where $n=1,3,\mathrm{5.....}$

When it covers a displacement of 20 m, it ends up at the diametrically opposite point from where it initially started. But as we do not know that whether the body has covered half a circle or one half or two and half and so on..... the distance it has covered will be $\frac{2\pi r}{2}\times n$ where $n=1or3or5..........2x+1$

so the speed of the body will be $\frac{10n\pi }{10s}=n\pi m/s$ where $n$ can be 1,3,5......