List of top Solid Mechanics Questions on Force of Friction asked in GATE XE

Consider two blocks, P of mass 100 kg and Q of mass 150 kg, resting as shown in the figure. The angle of the wedge is \(\theta = 30^\circ\). The coefficient of friction between the two blocks is \(\mu = 0.2\). Assume no friction exists at all other interfaces.
The minimum force required to move block P upward is \(W\).

Which one of the following options is closest to the correct magnitude of \(W\) (in N)?

A solid uniform rigid disk of mass $m$ and radius $R$ rolls without slipping along a horizontal surface $PQ$. The speed of the center of the disk is $v$. The disk then strikes a hurdle of height $\tfrac{3R}{20}$ at point $S$. During the impact, there is no rebound or slip at $S$ and no impulse from the surface $PQ$. The magnitude of the velocity of the center of the disk immediately after the impact is:

A slider moves in a frictionless slot and is connected via a spring OA. Given: spring stiffness = 2 kN/m, mass = 10 kg, unstretched spring length = 1 m. If released from rest at A, find velocity (m/s) when passing through B. (Rounded to nearest integer)

A truck moves at 20 m/s carrying a 1000 kg box. Coefficient of friction between box and platform is \(\mu = 0.25\). Find the shortest stopping distance so that the box does not slip. (round off to nearest integer).

Two identical mass-less beams AB and CD are clamped at their ends. The left end of beam CD rests on the right end of beam AB at point C (no friction). A uniformly distributed load of 800 N/m is applied on beam CD of span 1 m. Find the bending moment at end B of beam AB (in N·m). Round off to the nearest integer.

A spring–mass system having a mass $m$ and spring constant $k$, placed horizontally on a foundation, is connected to a vertically hanging mass $m$ with the help of an inextensible string as shown. Ignore pulley friction, and neglect pulley, string, and spring inertia. Gravity acts downward. The natural frequency of the system in rad/s is:

One end of a uniform rigid rod $OA$ of length $L$ and mass $m$ is attached to a frictionless hinge at $O$. The other end of the rod is connected to the roof at $B$ with a massless inextensible thread $AB$. Initially the rod is horizontal and at rest. The gravity is acting vertically downward as shown. Immediately after the thread $AB$ is cut, the reaction on the rod at $O$ is:

A mass \( m = 10 \, \text{kg} \) is attached to a spring as shown in the figure. The coefficient of friction between the mass and the inclined plane is 0.25. Assume that the acceleration due to gravity is \( 10 \, \text{m/s}^2 \) and that static and kinetic friction coefficients are the same. Equilibrium of the mass is impossible if the spring force is:

A rigid circular disc of radius 0.2 m and mass 10 kg rolls without slip on the ground at A. The coefficient of static friction \( \mu \) between ground and disc is 0.7. A torque \( T \) of 9 Nm acts on the disc as shown. Given acceleration due to gravity \( g = 10 \, \text{m/s}^2 \). The friction force (in N) acting on the disc (in integer) is \(\underline{\hspace{2cm}}\). \includegraphics[width=0.5\linewidth]{image16.png}