A cubical block of side L is placed on a rough horizontal surface with coefficient of friction μ. 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

A football of radius $R$ is kept on a hole of radius $r(r<R)$ made on a plank kept horizontally. One end of the plank is now lifted so that it gets tilted making an angle $\theta$ from the horizontal as shown in the figure below. The maximum value of $\theta$  so that the football does not start rolling down the plank satisfies (figure is schematic and not drawn to scale)

A $\sqrt{34} \mathrm{m}$ long ladder weighing $10 \mathrm{kg}$ leans on a frictionless wall. Its feet rest on the floor $3 \mathrm{m}$ away from the wall as shown in the figure. If $F_f$ and $F_w$ are the reaction forces of the floor and the wall, then ratio of $\frac{F_w}{F_f}$ will be :
(Use $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.)

A uniform rod of length $200 \mathrm{cm}$ and mass $500 \mathrm{g}$ is balanced on a wedge placed at $40 \mathrm{cm}$ mark. A mass of $2 \mathrm{kg}$ is suspended from the rod at $20 \mathrm{cm}$ and another unknown mass $m$ is suspended from the rod at $160 \mathrm{cm}$ mark as shown in the figure. Find the value of $m$ such that the rod is in equilibrium. $\left.(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A rod of length $L$ can rotate about end $0 .$ What is the work done if the rod is rotated by $180°$

One end of a horizontal uniform beam of weight $W$ and length $L$ is hinged on a vertical wall at point $O$ and its other end is supported by a light inextensible rope. The other end of the rope is fixed at point $Q$, at a height $L$ above the hinge at point $O$. A block of weight $\alpha W$ is attached at the point $P$ of the beam, as shown in the figure (not to scale). The rope can sustain a maximum tension of  $\left(2\sqrt{2}\right)W$. Which of the following statement(s) is(are) correct?

A bead of mass $\mathrm{m}$ stays at point $\mathrm{P}\left(\mathrm{a}, \mathrm{b}\right)$ on a wire bent in the shape of a parabola $y=C{x}^{\mathit{2}}$ and rotating with angular speed $\mathrm{\omega }$ (see figure). The value of $\omega$ is (neglect friction)

Shown in the figure is rigid and uniform one meter long rod $\mathrm{AB}$ held in horizontal position by two strings tied to its ends and attached to the ceiling. The rod is off mass $\text{'}\mathrm{m}\text{'}$ and has another weight of mass $2 \mathrm{m}$ hung at a distance of $75 \mathrm{cm}$ from $\mathrm{A}$. The tension in the string at $\mathrm{A}$ is:

Consider a uniform cubical box of side a on a rough floor that is to be moved by applying minimum possible force $\mathrm{F}$ at a point $\mathrm{b}$ 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 a box not to topple before moving is ________

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.

Consider an obese person bent forward on the ground whose center of mass is at O. The person's hands don't touch the ground. Then friction on the shoes

A uniform rod of mass m and length $l$ is suspended by means of two light inextensible strings as shown in figure. tension in one string immediately after the other string is cut is