# GATE Questions & Answers of Kinematics and Dynamics of Particles and of Rigid Bodies in Plane Motion

## What is the Weightage of Kinematics and Dynamics of Particles and of Rigid Bodies in Plane Motion in GATE Exam?

Total 19 Questions have been asked from Kinematics and Dynamics of Particles and of Rigid Bodies in Plane Motion topic of Engineering Mechanics subject in previous GATE papers. Average marks 1.53.

A force of 100 N is applied to the centre of a circular disc, of mass 10 kg and radius 1 m, resting on a floor as shown in the figure. If the disc rolls without slipping on the floor, the linear acceleration (in m/s2) of the centre of the disc is ________ (correct to two decimal places).

A partical of unit mass is moving on a plane. Its trajectory, in polar coordinates, is given by $\style{font-family:'Times New Roman'}{r(t)=t^2,\theta(t)\;=t}$, where t is time. The kinetic energy of the partical at time t=2 is

The following figure shows the velocity-time plot for a particle traveling along a staright line. The distance coverd by the particle from t = 0 to t = 5 s is ____________ m,

Two disks A and B with identical mass (m) and radius (R) are initialy at rest. They roll down from the top of identical inclined planes without slipping. Disk A has all of its mass concentrated at the rim, while Disk B has its mass uniformly distributed. At the bottom of the plane, the ratio of velocity  of the center of disk A to the velocity of the center of disk B is

A point mass M is released from rest and slides down a spherical bowl (of radius R) from a height H as shown in the figure below. The surface of the bowl is smooth (no friction). The velocity of the mass at the bottom of the bowl is

A rigid link PQ is undergoing plane motion as shown in the figure ($V_P$ and $V_Q$ are non - zero). $V_{QP}$ is the relative velocity of point Q with respect to point P.

Which one of the following is TRUE?

A circular disc of radius 100 mm and mass 1 kg, initially at rest at position A, rolls without slipping down a curved path as shown in figure. The speed $v$ of the disc when it reaches position B is _________ m/s.

Acceleration due to gravity g = 10 m/s2.

A rigid rod (AB) of length $L=\sqrt{2}$ m is undergoing translational as well as rotational motion in the x-y plane (see the figure). The point A has the velocity $V_{1\;}=\widehat i+2\widehat j$ m/s. The end B is constrained to move only along the x direction.

The magnitude of the velocity V2 (in m/s) at the end B is __________

A wheel of radius r rolls without slipping on a horizontal surface shown below. If The velocity of point P is 10 m/s in the horizontal direction, the magnitude of velocity of point Q (in m/s) is ________

The initial velocity of an object is 40 m/s. The acceleration $a$ of the object is given by the following expression:

$a=-0.1\;v,$

Where $v$ is the instantaneous velocity of the object. The velocity of the object after 3 seconds will be____.

The value of moment of inertia of the section shown in the figure about the axis-XX is

Figure shows a wheel rotating about O2. Two points A and B located along the radius of wheel have speeds of 80 m/s and 140 m/s respectively. The distance between the points A and B is 300 mm. The diameter of the wheel (in mm) is__________

A bullet spins as the shot is fired from a gun. For this purpose, two helical slots as shown in the figure are cut in the barrel. Projections A and B on the bullet engage in each of the slots.

Helical slots are such that one turn of helix is completed over a distance of 0.5 m. If velocity of bullet when it exits the barrel is 20 m/s, its spinning speed in rad/s is _______.

A  circular object of radius r rolls without slipping on a horizontal level floor with center having velocity V. The velocity at the point of contact between the object and floor is

An annular disc has a mass m, inner radius R and outer radius 2R. The disc rolls on a flat surface without slipping. If the velocity of the center of mass is v, the kinetic energy of the disc is

A point mass is executing simple harmonic motion with an amplitude of 10 mm and frequency of 4 Hz. The maximum acceleration (m/s2) of the mass is _______

A block weighing 981 N is resting on a horizontal surface. The coefficient of friction between the block and the horizontal surface is µ = 0.2.A vertical cable attached to the block provides partial support as shown. A man can pull horizontally with a force of 100 N. What will be the tension, T (in N) in the cable if the man is just able to move the block to the right?

A straight rod of length L(t), hinged at one end and freely extensible at the other end, rotates through an angle about the hinge. At time t, L(t) =1 m,$\dot L\left(t\right)$ = 1 m/s, $\theta \left(t\right)=\frac{\mathrm{\pi }}{4}$ rad and $\dot\theta\left(t\right)$= 1 rad/s. The magnitude of the velocity at the other end of the rod is