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

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 ($\style{font-family:'Times New Roman'}{\left(V_{P\;}and\;V_Q\;are\;non-zero\right)}. $\style{font-family:'Times New Roman'}{V_{QP}}$ 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=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  θt about the hinge. At time t, L(t) =1 m,$\dot L\left(t\right)$ = 1 m/s, θt=π4 rad and $\dot\theta\left(t\right)$= 1 rad/s. The magnitude of the velocity at the other end of the rod is

A circular disk of radius R rolls without slipping at a velocity v. The magnitude of the velocity at point P (see figure) is