List of top Solid Mechanics Questions on Particle kinematics and dynamics asked in GATE XE

Two cars P and Q are travelling on a straight path and are 60 m apart. Car P moves with \(36~\text{km/h}\), car Q moves with \(18~\text{km/h}\). At \(t=0\), driver in car P applies brakes, uniform deceleration occurs, and collision happens after \(30~\text{s}\). Find the correct velocity (in m/s) of car P just before collision.
A ball of mass \(5m\) approaches a stationary ball of mass \(m\) with a horizontal velocity of \(2 \, m/s\) from left to right. After a perfectly elastic central collision, the horizontal velocity of the heavier ball is \(1 \, m/s\) from left to right. Which one of the following statements, regarding the velocity (in m/s) of the lighter ball after impact, is TRUE?
A thin-walled, closed cylindrical vessel of inside diameter $d$ and wall thickness $t$ contains a fluid under pressure $p$. The figure shows a part of the cylindrical vessel; end caps are not shown. Consider the small element with sides parallel and perpendicular to the axis of the cylinder. The stresses $\sigma_1$ and $\sigma_2$ are:
A massless rigid rod $OP$ of length $L$ is hinged frictionlessly at $O$. A concentrated mass $m$ is attached to end $P$ of the rod. Initially, the rod $OP$ is horizontal. Then, it is released from rest. There is gravity as shown. The rod acquires an angular velocity as it swings. The clockwise angular velocity of the rod, when it first reaches the vertical position as shown, is:
A coronavirus droplet of mass 1 microgram ejects from the mouth of a patient with a velocity of 0.7 m/s and travels through air. The gravitational force experienced by it can be neglected due to the buoyancy effect. However, the droplet experiences air drag force proportional to its velocity and the drag coefficient is given as 1.0 μN-s/m. The distance travelled by the droplet before its velocity drops to 10% of its initial velocity (in m, rounded off to two decimal places) is \(\underline{\hspace{2cm}}\).
A rigid rod OA rotates clockwise at an angular velocity of 10 rad/s. A bead B (OB = 1 m) translates outward on the rod at a speed of 5 m/s and acceleration 2.5 m/s² (both quantities with respect to the rod). The Coriolis component of acceleration is
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