(A) To topple the prism, it must rotate about the edge $C$.The force $F$ is applied at the top vertex $A$ at a height $h = a\frac{\sqrt{3}}{2}$ from t

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(A) To topple the prism, it must rotate about the edge $C$.The force $F$ is applied at the top vertex $A$ at a height $h = a\frac{\sqrt{3}}{2}$ from the base.The weight $mg$ acts at the center of mass, which is at a horizontal distance of $a/2$ from the edge $C$.For the prism to be on the verge of toppling, the torque due to force $F$ about point $C$ must balance the torque due to gravity $mg$ about point $C$.Torque due to $F$ about $C$ = $F \times h = F \times a\frac{\sqrt{3}}{2}$.Torque due to $mg$ about $C$ = $mg \times \frac{a}{2}$.Equating the torques: $F \times a\frac{\sqrt{3}}{2} = mg \times \frac{a}{2}$.Solving for $F$, we get $F = \frac{mg}{\sqrt{3}}$.

Class 11 Physics System of Particles and Rotational Motion Toppling and Instantaneous Axis of Rotation

Medium

An equilateral prism of mass $m$ rests on a rough horizontal surface with coefficient of friction $\mu$. A horizontal force $F$ is applied on the prism at the top vertex $A$ as shown in the figure. If the coefficient of friction is sufficiently high so that the prism does not slide before toppling, then the minimum force required to topple the prism is $-$

A
$\frac{mg}{\sqrt{3}}$
B
$\frac{mg}{4}$
C
$\frac{\mu mg}{\sqrt{3}}$
D
$\frac{\mu mg}{4}$

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Class 11 Questions

Class 11

Physics Questions

Chapter

System of Particles and Rotational Motion

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Toppling and Instantaneous Axis of Rotation

The instantaneous velocity of point $B$ of a rod of length $0.5 \ m$ is $3 \ m/s$ at an angle of $30^{\circ}$ with the rod as shown. Find the angular velocity of the rod such that the velocity of end $A$ is minimum.

DifficultAP EAMCET 2005

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$A$ cube with sides of length $2a$ and mass $M$ is moving with an initial speed $v_0$ along a frictionless table. When the cube reaches the end of the table it is caught abruptly by a short lip and begins to rotate. The minimum speed $v_0$ such that the cube falls off the table is

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Calculate the minimum amount of work necessary to overturn a crate of mass $100 \ kg$,first about edge $AB$,then about edge $A_1B_1$. The dimensions of the crate are given in the figure. (Assume $g = 10 \ m/s^2$) (in $J$)

Medium

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$A$ ladder of length $L$ is slipping with its ends against a vertical wall and a horizontal floor. At a certain moment,the speed of the end in contact with the horizontal floor is $v$ and the ladder makes an angle $\alpha = 30^o$ with the horizontal. Then the speed of the ladder's center must be

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$A$ disc is rolling (without slipping) on a horizontal surface. $C$ is its center and $Q$ and $P$ are two points on the disc such that $Q$ is further from the contact point $O$ than $C$,and $P$ is closer to the contact point $O$ than $C$. Let $V_P, V_Q$ and $V_C$ be the magnitudes of the velocities of points $P, Q$ and $C$ respectively,then:

Medium

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The instantaneous velocity of point $B$ of a rod of length $0.5 \ m$ is $3 \ m/s$ at an angle of $30^{\circ}$ with the rod as shown. Find the angular velocity of the rod such that the velocity of end $A$ is minimum.

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