A particle describes a horizontal circle of r | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the semi-vertical angle of the cone be $	heta$. From the geometry of the cone,we have $	an 	heta = \frac{r}{h}$.The forces acting on the pa

Vedclass · Accepted Answer

$\sqrt{g h}$

Vedclass · Answer

(C) Let the semi-vertical angle of the cone be $	heta$. From the geometry of the cone,we have $	an 	heta = \frac{r}{h}$.The forces acting on the particle are its weight $mg$ acting downwards and the normal reaction $N$ from the surface of the cone acting perpendicular to the surface.Resolving the normal reaction $N$ into horizontal and vertical components:Vertical component: $N \cos 	heta = mg$  --- $(i)$Horizontal component (providing the centripetal force): $N \sin 	heta = \frac{mv^2}{r}$ --- (ii)Dividing equation (ii) by equation $(i)$:$\frac{N \sin 	heta}{N \cos 	heta} = \frac{mv^2/r}{mg}$$	an 	heta = \frac{v^2}{rg}$Substituting $	an 	heta = \frac{r}{h}$ into the equation:$\frac{r}{h} = \frac{v^2}{rg}$$v^2 = \frac{r^2 g}{h}$$v = r \sqrt{\frac{g}{h}}$Wait,re-evaluating the geometry: If $	heta$ is the angle the slant surface makes with the horizontal,then $	an 	heta = \frac{h}{r}$.Then $\frac{h}{r} = \frac{v^2}{rg} \implies v^2 = gh \implies v = \sqrt{gh}$.

$A$ particle describes a horizontal circle of radius $r$ on the smooth surface of an inverted cone as shown. The height of the plane of the circle above the vertex is $h$. The speed of the particle should be

Similar Questions

An object of mass $m$ moves with constant speed in a circular path of radius $R$ under the action of a force of constant magnitude $F$. The kinetic energy of the object is ............

Two stones of masses $m$ and $3m$ are whirled in horizontal circles,the heavier one in a radius of $(r/3)$ and the lighter one in a radius of $r$. The tangential speed of the lighter stone is $n$ times that of the heavier stone when they experience the same centripetal force. The value of $n$ is:

$A$ string of length ' $\ell$ ' fixed at one end carries a mass 'm' at the other end. The string makes $\frac{3}{\pi}$ revolutions per second around the vertical axis through the fixed end as shown in the figure. The tension '$T$' in the string is:

$A$ block of $200\, g$ mass moves with a uniform speed in a horizontal circular groove,with vertical side walls of radius $20\, cm$. If the block takes $40\, s$ to complete one round,the normal force by the side walls of the groove is

Vedclass Test Series

Exam Paper Generator

Online Exam Module