Toppling

A uniform rectangular box of dimensions $\left(40 \mathrm{cm}\times 20 \mathrm{cm}\right)$ is kept on horizontal smooth surface at a distance $10 \mathrm{m}$ from a wall. A constant force $F$ is applied at the highest point as shown. The minimum time (in $\mathrm{s}$) to reach the wall without causing the box to rotate is:    $\left(g=9.8 \mathrm{m} {\mathrm{s}}^{-2}\right)$

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A truck is moving with acceleration $a$. A box of dimensions $l$ and $b$ is kept on it. If the box does not slide, the maximum acceleration for it to remain in equilibrium (with respect to the truck) is

Consider a uniform cubical box of side $a$ on a rough floor that is to be moved by applying minimum possible force $F$ at a point $b$ above its centre of mass (see figure). If the coefficient of friction is $\mu =0.4,$ the maximum possible value of $100\times \frac{\mathrm{b}}{\mathrm{a}}$ for box not to topple before moving is ________

A uniform cube of side a & mass m rests on a rough horizontal table. A horizontal force $F$ is applied normal to one of the faces at a point that is directly above the centre of the face, at a height $3 a/4$ above the base. The minimum value of $F$ for which the cube begins to tip about an edge is -----.(assume that cube does not slide).

An uniform semi-solid sphere is placed with flat surface on rough inclined plane as shown in the figure. If the friction is large for no sliding, then the minimum angle $\mathrm{\theta }$ at which toppling occur is,

An engineer is designing a conveyor system for loading lay bales into a wagon. Each bale is 0.25 m wide, 0.50 m high, and 0.80 m long (the dimension perpendicular to the plane of the figure), with mass 30.0 kg. The center of gravity of each bale is at its geometrical center. The coefficient of static friction between a bale and the conveyor belt is 0.60, and the belt moves with constant speed. The angle $\text{β}$ of the conveyor is slowly increased. At some critical angle a bale will tip (if it doesn't slip first), and at some different critical angle it will slip (if it doesn't tip first).

Find the first critical angle (In the same conditions) at which it tips..

Find the maximum height at which $F$ acts, so that sliding and tipping are equally likely to occur.

Find the greatest height at which force $F$ may be applied to slide the block without tipping over.

A cubical block of mass $6 \mathrm{kg}$ and side $16.1 \mathrm{cm}$ is placed on frictionless horizontal surface. It is hit by a cube at the top to impart impulse in horizontal direction. Minimum impulse(to the nearest integer in $\mathrm{kg} \mathrm{m} {\mathrm{s}}^{-1}$) imparted to topple the block must be greater than –

A cubical block of mass $6 \mathrm{kg}$ and side $16.1 \mathrm{cm}$ is placed on frictionless horizontal surface. It is hit by a cube at the top to impart impulse in horizontal direction. Minimum impulse(to the nearest integer in $\mathrm{kg} \mathrm{m} {\mathrm{s}}^{-1}$) imparted to topple the block must be greater than –

A cubical block of mass $6 \mathrm{kg}$ and side $16.1 \mathrm{cm}$ is placed on frictionless horizontal surface. It is hit by a cube at the top to impart impulse in horizontal direction. Minimum impulse(to the nearest integer in $\mathrm{kg} \mathrm{m} {\mathrm{s}}^{-1}$) imparted to topple the block must be greater than –

A cubical block of mass $6 \mathrm{kg}$ and side $16.1 \mathrm{cm}$ is placed on frictionless horizontal surface. It is hit by a cube at the top to impart impulse in horizontal direction. Minimum impulse(to the nearest integer in $\mathrm{kg} \mathrm{m} {\mathrm{s}}^{-1}$) imparted to topple the block must be greater than –

A regular polygon of n sides is placed on a rough surface vertically as such one of the side of regular polygon touches the surface. A force is applied horizontally at the top. The chosen value of $n$ are $3, 5$ and $8$. For which value of $n$, the polygon first is likely to topple

Two cubes $A$ and $B$ of same shape, size and mass are placed on a rough surface in the same manner. Equal forces are applied on both cubes. But at the cube $A$, the force is applied at the top in a horizontal direction. But at the cube $B$ just above the centre of mass of the cube in the same manner. Then

A bullet of mass m moving with a speed ν hits a stationary block of mass M at the topmost point and gets embedded in it. If friction is sufficient to prevent slipping then the block.

In the case of toppling of the body about the point $\mathrm{A}$. (Shown in the figure)

A cubical block of mass $m$ and side $L$ rests on a rough horizontal surface with coefficient of friction $\mathrm{\mu }$ . A horizontal force $F$ is applied on the block as shown. If the coefficient of friction is sufficiently high so that the block does not slide before toppling, the minimum force required to topple the block is

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

An equilateral prism of mass $\mathrm{m}$ rests on a rough horizontal surface with coefficient of friction $\mathrm{\mu }$ . A horizontal force $\mathrm{F}$ is applied on the prism 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 right circular cone with semi vertical angle ' $\mathrm{\alpha }$ ' rest on a rough inclined plane. As angle of inclination $\mathrm{\theta }$ increases, cone will slides before it topples over if coefficient of friction -