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A body is in equilibrium on a rough inclined plane of which the coefficient of friction is $(1/\sqrt{3})$ . The angle of inclination of the plane is gradually increased. The body will be on the point of sliding downwards, when the inclinician of the plane reaches
A body of weight 40 kg rests on a rough horizontal plane, whose coefficient of friction is 0.25. The least force which acting horizontally would move the body is
A hemi-spherical shell rests on a rough inclined plane, whose angle of friction is $\lambda $ , the inclination of the plane base of the rim to the horizon cannot be greater than
A uniform ladder of length 70m and weight W rests against a vertical wall at an angle of ${{45}^{o}}$ with the wall. The coefficient of friction of the ladder with the ground and the wall are $\frac{1}{2}$ and $\frac{1}{3}$ respectively. A man of weight $\frac{W}{2}$ climbs the ladder without slipping. The height in metre to which he can climb is
A body is on the point of sliding down an inclined plane under its own weight. If the inclination of the plane to the horizon be ${{30}^{o}}$ , the angle of friction will be
The end of a heavy uniform rod AB can slide along a rough horizontal rod AC to which it is attached by a ring. B and C are joined by a string. If $\angle ABC$ be a right angle, when the rod is on the point of sliding,$\mu $ the coefficient of friction and $\alpha $ the angle between AB and the vertical, then
A solid cone of semi- vertical angle $\theta $ is placed on a rough inclined plane. If the inclination of the plane is increased slowly and $\mu < 4 \tan \theta $ , then
A circular cylinder of radius r and height h rests on a rough horizontal plane with one of its flat ends on the plane. A gradually increasing horizontal force is applied through the centre of the upper end. If the coefficient of friction is $\mu $ , the cylinder will topple before sliding, if
A uniform beam AB of weight W is standing with the end B on a horizontal floor and end A leaning against a vertical wall. The beam stands in a vertical plane perpendicular to the wall inclined at ${{45}^{o}}$ to the vertical, and is in the position of limiting equilibrium. If the two points of contact are equally rough, then the coefficient of friction at each of them is
A body is pulled up an inclined rough plane. Let $\lambda $ be the angle of friction. The required force is least when it makes an angle $k\lambda $ with the inclined plane, where $k=$

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