Find minimum height of obstacle so that sphere can stay in equilibrium.

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6.System of Particles and Rotational Motion

hard

Find minimum height of obstacle so that the sphere can stay in equilibrium.

$\frac{R}{{1 + \cos \theta }}$

$\frac{R}{{1 + \sin \theta }}$

$R (1- sin\theta )$

$R (1 - cos\theta )$

Solution

The sphere is on the verge of toppling when a line of action of weight passes through the edge. The equilibrium is because of the line of action of weight and the normal reaction provided by the edge.

$\cos \theta=\frac{(R-h)}{R}$

$h=R-R \cos \theta$

Standard 11

Physics

$3\; m$ long ladder wetghing $20 kg$ leans on a frictionless wall. Its feet rest on the floor $1\; m$ from the wall as shown in Figure Find the reaction forces of the wall and the floor.

medium

A mass $'m'$ is supported by a massless string wound around a uniform hollow cylinder of mass $m$ and radius $R$. If the string does not slip on the cylinder, with what acceleration will the mass fall on release?

medium

(JEE MAIN-2014)

The resultant of the system in the figure is a force of $8N$ parallel to the given force through $R$. The value of $PR$ equals to

medium

Two particles of mass $m$ each are fixed at the opposite ends of a massless rod of length $5m$ which is oriented vertically on a smooth horizontal surface and released. Find the displacement of the lower mass on the ground when the rod makes an angle of $37^o$ with the vertical. …….. $m$

medium

Write the conditions for equilibrium of a rigid body.

hard

Find minimum height of obstacle so that the sphere can stay in equilibrium.

Solution

Similar Questions

$3\; m$ long ladder wetghing $20 kg$ leans on a frictionless wall. Its feet rest on the floor $1\; m$ from the wall as shown in Figure Find the reaction forces of the wall and the floor.

A mass $'m'$ is supported by a massless string wound around a uniform hollow cylinder of mass $m$ and radius $R$. If the string does not slip on the cylinder, with what acceleration will the mass fall on release?

The resultant of the system in the figure is a force of $8N$ parallel to the given force through $R$. The value of $PR$ equals to

Two particles of mass $m$ each are fixed at the opposite ends of a massless rod of length $5m$ which is oriented vertically on a smooth horizontal surface and released. Find the displacement of the lower mass on the ground when the rod makes an angle of $37^o$ with the vertical. …….. $m$

Write the conditions for equilibrium of a rigid body.

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