Question
A particle of mass $m$ is rotating in a plane in circular path of radius $r$. Its angular momentum is $L$. The centripetal force acting on the particle is(a) $L^{2} / m r$(b) $L^{2} m / r$(c) $L^{2} / m^{2} r^{2}$(d) $L^{2} / m r^{3}$
Step 1
Step 1: The centripetal force $F$ acting on a particle moving in a circular path of radius $r$ is given by the formula $F = m v^{2} / r$, where $m$ is the mass of the particle and $v$ is the velocity of the particle. Show more…
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$\Lambda$ body of mass $m$ is moving in a plane along a circle of radius $r$. Its angular momentum about the axis of rotation is $L$. The centripetal force acting on the particle will be (a) $\frac{L^{2}}{m r}$ (b) $\frac{L^{2}}{m r^{3}}$ (c) $\frac{L^{2} m}{r}$ (d) $\frac{L^{2}}{m r^{2}}$
Rotational and Rolling Motion
Section B
A particle of mass $m$ is describing a circular path of radius $r$ with uniform speed. If $L$ is the angular momentum of the particle about the axis of the circle, the kinetic energy of the particle is given by [CPMT 1995] (a) $L^{2} / m r^{2}$ (b) $L^{2} / 2 m r^{2}$ (c) $2 L^{2} / m r^{2}$ (d) $m r^{2} L$
A particle of mass $m$ is revolving in a horizontal circle of radius $r$ with constant angular speed $\omega .$ The areal velocity of the particle is (a) $r^{2} \omega$ (b) $r^{2} \theta$ (c) $\frac{r^{2} \omega}{2}$ (d) $\frac{r \omega^{2}}{2}$
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