List of top Solid Mechanics Questions

The figure shows a rod PQ, hinged at P, rotating counter-clockwise with a uniform angular speed of 15 rad/s. A block R translates along a slot cut out in rod PQ. At the instant shown the distance \( PR = 0.5 \, {m} \) and \( \theta = 60^\circ \). The relative velocity of R with respect to the rod PQ is 5 m/s at the instant shown. The relative acceleration of R with respect to the rod PQ is zero at the instant shown. 
Which one of the following is the CORRECT magnitude of the absolute acceleration (in m/s\(^2\)) of block R? 

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

A force of \( P = 100 \, {N} \) is applied at the ends of the pliers as shown in the figure. Neglecting friction, the force exerted by the upper jaw on the workpiece is ........... N (in integer). 

For a certain linear elastic isotropic material, the Young’s modulus is 140 GPa and the shear modulus is 50 GPa. The Poisson’s ratio for the material is ........... (rounded off to two decimal places).

Consider a beam with a square box cross-section as shown in the figure. The outer square has a length of 10 mm. The thickness of the section is 1 mm. The area moment of inertia about the x-axis is ........... mm\(^4\) (in integer). 

The natural frequency of a spring-mass system is 10 rad/s. Which of the following statements is/are CORRECT?

Two cars P and Q are travelling on a straight path and are 60 m apart as shown in the figure; Car P is moving with a constant velocity of 36 kmph, while car Q is moving at a constant velocity of 18 kmph. At this instant, the driver in car P applies the brake and collision occurs with car Q after 30 seconds. Assuming uniform deceleration due to braking, which one of the following is the CORRECT velocity (in m/s) of the car P just before the collision? 

The two-dimensional state of stress, in an infinitesimal element, is given by \[ \sigma_{xx} = 800 \, {MPa}, \sigma_{xy} = 300 \, {MPa}, \sigma_{yy} = 0 \, {MPa}. \] Which one of the following options is the maximum shear stress (in MPa) in the element?

The Mohr’s circle corresponding to an infinitesimal element is shown in the figure. The plane PQ in the infinitesimal element, at an angle of \( \theta \) from the x-axis, is in a state of pure shear. Which one of the following values of \( \theta \) (in degrees) is CORRECT?

Which one of the following vertical columns, of circular cross-section, sustains the highest load without buckling?
Given below are two statements:
Statement I: If axial load is less than crippling load, the column is in stable equilibrium in the straight position.
Statement II: The equilibrium of the column does not depend upon the crippling load.
In the light of the above statements, choose the correct answer from the options given below: