Recent questions in Mechanics of rigid bodies

Two axial members, namely $\text{OP}$ and $\text{OQ}$, are pin joined at $\text{O}$ as shown in the figure. A force $F$ acts at point $\text{P}$ along the positive $x$ di...

Two smooth drums each weighing $W$ and radius, $r$ are connected by a stiff rope of length, $h$ as shown in the figure. Force $F$ is applied using a massless lever (RS) o...

A rigid block of mass $m$ on a horizontal surface is connected to three springs each having spring constant $k$ as shown in the figure.Which one of the following is the C...

A car is moving on a horizontal surface in a straight line with a constant velocity of $3 \mathrm{~m} / \mathrm{s}$. A ball is thrown vertically upwards at time $t=0$ fro...

A cart of weight $(W) 5 \mathrm{kN}$, stands on an inclined smooth surface at an angle $(\theta)$ of $45^{\circ}$ as shown in the figure. The cart is maintained in equili...

The force $(F)$ acting on the block, as shown in the figure is $2\text{N}$. The stiffness of the spring ( $k$ ) is $100 \mathrm{~N} / \mathrm{m}$.Assume that the block is...

Which one of the following options is the CORRECT absolute value of the bending moment at $\text{R}$ in the frame as shown in the figure?$0$$\mathrm{Fl}$$2 \text{Fl}$$3 \...

A spring of stiffness $k$ is connected to the center of a homogeneous right circular cylinder of radius $r$ placed on a horizontal surface as shown in the figure. The cyl...

The point $\text{Q}$ of a thin rigid equilateral triangular plate $\text{PQR}$ is constrained to move in a horizontal channel. Point $\text{P}$ of the same plate is const...

​​​A ball of mass $5 \mathrm{m}$ approaches a stationary ball of mass $\mathrm{m}$ with a horizontal velocity of $2 \mathrm{~m} / \mathrm{s}$ from left to right. After a ...

​​​​​​Two cars $\text{P}$ and $\text{Q}$ are travelling on a straight path and are $60 \: \mathrm{m}$ apart as shown in the figure; Car $\text{P}$ is moving with a consta...

Consider two blocks, $\mathbf{P}$ of mass $100 \: \mathrm{kg}$ and $\mathbf{Q}$ of mass $150 \: \mathrm{ kg}$, resting as shown in the figure. The angle $\theta=30^{\circ...

​​​​The figure shows a rod $\text{PQ}$, hinged at $\text{P}$, rotating counter-clockwise with a uniform angular speed of $15 \: \mathrm{rad} / \mathrm{s}$. A block $R$ tr...

​​​The frame shown in the figure is loaded at $\text{S}$ with a force of $2000 \: \text{N}$. The reactions at $\text{T}$ are denoted by $\text{T}_{x}$ and $\text{T}_{y}$,...

An electric motor's rotor is spinning at $1500 \: \mathrm{rpm}$ when its load and power are cutoff. The rotor which has a mass of $50 \: \mathrm{ kg}$ and a radius of gyr...

An $\text{L}$-shaped rigid member is fixed at the midpoint of a simply-supported beam, as shown in figure $\text{(i)}$. The member is subjected to a vertically downward f...

A block of weight $W$, placed on a surface, is subjected to a horizontal force $P$ as shown in the figure. The line of action of force $P$ passes through the center-ofgra...

An ice-skater starts spinning during her performance. As she retracts her arms and legs closer to her body, her angular velocity __________.increasesdecreasesremains the ...

A particle of mass $1$ kg is attached to one end of a spring having stiffness of $125$ $\mathrm{N} / \mathrm{m}$. The free length of the spring is $100$ mm . The system i...

A rigid bar PQR is hinged at its end P . As shown in the figure, the bar is pinconnected through two identical links QS and RT at points Q and R , respectively. The other...

A pin-jointed truss has a pin support at the point E and a roller support at the point F. A horizontal force P is applied at pin H as shown in the figure. Which one of th...

Two identical rigid slender bars of length $2$ L and mass $m$ are acted upon by a transverse force F at one of the ends as shown in the figure. In the first case, the bar...

A rigid massless bar $\text{PQR}$ is hinged at its end $\text{P}$ and supported through a spring of stiffness $k$ at point $\text{Q}$. A vertically downward force $W=560 ...

A turn-table is rotating about its center with an angular velocity of $2 \mathrm{rad} / \mathrm{s}$ in the counter-clockwise direction. There is a groove in the turn-tabl...

The system shown in the figure is in static equilibrium. The spring is massless and has a spring constant of $\mathrm{K}=1 \mathrm{kN} / \mathrm{m}$. The free length of t...

A square block of side $1$ m and mass $10$ kg is resting on a horizontal surface. The coefficient of static friction between the block and the surface is $0.75$. A horizo...

\begin{tabular}{l}Q. 66 \\A plane truss is simply supported at $P$ and $R$ as shown. A downward force $F$ is \\applied at hinge $Q$. The axial force developed in member $...

\begin{tabular}{l}Q.67 A massless rigid rod $O P$ of length $L$ is hinged frictionlessly at $O$. A concentrated \\mass $m$ is attached to end $P$ of the rod. Initially, t...

Q. 72 A rod is subjected to three forces as shown in the figure on the left. An equivalentforce system with forces $F_{1}, F_{2}$ and moment $M$ is shown in the figure on...

\begin{tabular}{|c|c|}\hline Q. 75 & \begin{tabular}{l}A solid uniform rigid disk of mass $m$ and radius $R$ rolls without slipping along a \\horizontal surface $\mathrm{...

Q. 81 A steel ball of mass $m=10 \mathrm{~kg}$ is suspended from the ceiling of a moving carriage by two inextensible strings making $60^{\circ}$ with the horizontal as s...

Q. 82 A block of mass $m=10 \mathrm{~kg}$ is lying on an inclined plane $\mathrm{PQ}$. The mass isrestrained from sliding down the inclined plane by a force $F$. The coef...

Q. 83A spherical rigid ball of mass $10 \mathrm{~kg}$ is moving with a speed of $2 \mathrm{~m} / \mathrm{s}$ in thedirection shown. The ball collides with a rigid frictio...

Q. 170 Two balls each of $5 \mathrm{~cm}$ in diameter are placed $200 \mathrm{~m}$ apart on a horizontal frictionless plane at $45^{\circ} \mathrm{N}$. The balls are impu...