Sand is to be piled up on a horizontal ground | vedclass

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

Question

(D) Let $h$ be the height of the sand cone with base radius $R$. The angle of repose $\alpha$ is the maximum angle at which the sand can be piled with

Vedclass · Accepted Answer

$\frac{\mu \pi R^3}{3}$

Vedclass · Answer

(D) Let $h$ be the height of the sand cone with base radius $R$. The angle of repose $\alpha$ is the maximum angle at which the sand can be piled without slipping. This angle is related to the coefficient of static friction $\mu$ by $	an \alpha = \mu$.In the cone,the angle $\alpha$ is formed by the slant height with the horizontal ground. From the geometry of the cone,$	an \alpha = \frac{h}{R}$.Equating the two expressions for $	an \alpha$,we get $\frac{h}{R} = \mu$,which implies $h = \mu R$.The volume $V$ of a cone is given by $V = \frac{1}{3} \pi R^2 h$.Substituting $h = \mu R$ into the volume formula,we get $V_{\max} = \frac{1}{3} \pi R^2 (\mu R) = \frac{\mu \pi R^3}{3}$.

Sand is to be piled up on a horizontal ground in the form of a regular cone of a fixed base of radius $R$. The coefficient of static friction between the sand layers is $\mu$. The maximum volume of the sand that can be piled up in the form of a cone without slipping on the ground is

Similar Questions

Starting from rest,the time taken by a body sliding down on a rough inclined plane at $45^{\circ}$ with the horizontal is twice the time taken to travel on a smooth plane of the same inclination and same distance. Then the coefficient of kinetic friction is

$A$ block of mass $0.1 \, kg$ is held against a wall by applying a horizontal force of $5 \, N$ on the block. If the coefficient of friction between the block and the wall is $0.5$,the magnitude of the frictional force acting on the block is ........ $N$.

$A$ body starts from rest on a long inclined plane of slope $45^o$. The coefficient of friction between the body and the plane varies as $\mu = 0.3x$,where $x$ is the distance travelled down the plane. The body will have maximum speed (for $g = 10 \ m/s^2$) when $x = $ ........ $m$.

$A$ body is made to move up along an inclined plane of inclination $30^{\circ}$ and the coefficient of friction is $0.5$. Then its retardation is ($g$ = acceleration due to gravity).

$A$ block slides down an inclined plane with an acceleration $g/2$ as shown in the figure. Then the coefficient of kinetic friction is

Vedclass Test Series

Exam Paper Generator

Online Exam Module