kinematics

A horizontal disk has a radial frictionless slot in which a small block is confined to slide. The disk turns anticlockwise about its centre with a constant angular velocity of 3 ra...

A rigid slender bar, AB, is sliding against two mutually perpendicular frictionless walls, as shown in the figure below. The velocity of A in the downward direction at a given inst...

A rigid circular disc of radius r (in m) is rolling without slipping on a flat surface as shown in the figure below. The angular velocity of the disc is ω (in rad s⁻¹). The velocit...

An offset slider-crank mechanism is shown in the figure below. The length of the stroke of the slider is ________ mm (rounded off to nearest integer).

Two cars, $P$ and $Q$, start from a point $X$ in India at 10 AM . Car $P$ travels North with a speed of $25 \mathrm{~km} / \mathrm{h}$ and car Q travels East with a speed of $30 \m...

Consider a velocity field $\vec{V}=3 z \hat{i}+0 \hat{j}+C x \hat{k}$, where $C$ is a constant. if the flow is irrotational, the value of C is ________ (rounded off to 1 decimal pl...

A ram in the form of a rectangular body of size l = 9 m and b = 2 m is suspended by two parallel ropes of lengths 7 m. Assume the center-of-mass of the body is at its geometric cen...

At the instant when OP is vertical and AP is horizontal, the link OD is rotating counter clockwise at a constant rate $\omega$ = 7 rad/s. Pin P on link OD slides in the slot BC of...

A spherical ball weighing 2 kg is dropped from a height of 4.9 m onto an immovable rigid block as shown in the figure. If the collision is perfectly elastic, what is the momentum v...

The figure shows a wheel rolling without slipping on a horizontal plane with angular velocity $\omega_1$. A rigid bar PQ is pinned to the wheel at P while the end Q slides on the f...

A tiny temperature probe is fully immersed in a flowing fluid and is moving with zero relative velocity with respect to the fluid. The velocity field in the fluid is $\vec V = (2x)...

A steady two-dimensional flow field is specified by the stream function ψ = kx 3 y, where x and y are in meters and the constant k = 1 m -2 s -1 . The magnitude of acceleration at...

Consider the mechanism shown in the figure. There is rolling contact without slip between the disc and ground. Select the correct statement about instantaneous centers in the mecha...

The Whitworth quick return mechanism is shown in the figure with link lengths as follows: OP = 300 mm, OA = 150 mm, AR = 160 mm, RS = 450 mm. The quick return ratio for the mechani...

A rigid triangular body, PQR, with sides of equal length of 1 unit moves on a flat plane. At the instant shown, edge QR is parallel to the x-axis, and the body moves such that velo...

A flat-faced follower is driven using a circular eccentric cam rotating at a constant angular velocity \omega. At time t = 0, the vertical position of the follower is y(0) = 0, and...

Water flows through a pipe with a velocity given by $\vec{V} = (\frac{4}{t} + x + y)\hat{j}$ m/s, where $\hat{j}$ is the unit vector in the y direction, $t (> 0)$ is in seconds, an...

In a four bar planar mechanism shown in the figure, AB = 5 cm, AD = 4 cm and DC = 2 cm. In the configuration shown, both AB and DC are perpendicular to AD. The bar AB rotates with...

The crank of a slider-crank mechanism rotates counter-clockwise (CCW) with a constant angular velocity ω, as shown. Assume the length of the crank to be r. Using exact analysis, th...

A four bar mechanism is shown in the figure. The link numbers are mentioned near the links. Input link 2 is rotating anticlockwise with a constant angular speed \omega_2. Length of...

In a slider-crank mechanism, the lengths of the crank and the connecting rod are 100 mm and 160 mm, respectively. The crank is rotating with an angular velocity of 10 radian/s coun...

The following figure shows the velocity-time plot for a particle traveling along a straight line. The distance covered by the particle from $t = 0$ to $t = 5$ s is ________ m.

A four bar mechanism is made up of links of length 100, 200, 300 and 350 mm. If the 350 mm link is fixed, the number of links that can rotate fully is ________.

A ball is dropped from rest from a height of 1 m in a frictionless tube as shown in the figure. If the tube profile is approximated by two straight lines (ignoring the curved porti...

A point mass is shot vertically up from ground level with a velocity of 4 m/s at time, t = 0. It loses 20% of its impact velocity after each collision with the ground. Assuming tha...

An epicyclic gear train is shown in the figure below. The number of teeth on the gears A, B and D are 20, 30 and 20, respectively. Gear C has 80 teeth on the inner surface and 100...

Block 2 slides outward on link 1 at a uniform velocity of 6 m/s as shown in the figure. Link 1 is rotating at a constant angular velocity of 20 radian/s counterclockwise. The magni...

A rigid rod of length 1 m is resting at an angle $\theta = 45^\circ$ as shown in the figure. The end P is dragged with a velocity of $U = 5$ m/s to the right. At the instant shown,...

In a cam-follower, the follower rises by h as the cam rotates by δ (radians) at constant angular velocity ω (radians/s). The follower is uniformly accelerating during the first hal...

In an epicyclic gear train, shown in the figure, the outer ring gear is fixed, while the sun gear rotates counterclockwise at 100 rpm. Let the number of teeth on the sun, planet an...

For an inline slider-crank mechanism, the lengths of the crank and connecting rod are 3 m and 4 m, respectively. At the instant when the connecting rod is perpendicular to the cran...

From the time the front of a train enters a platform, it takes 25 seconds for the back of the train to leave the platform, while travelling at a constant speed of 54 km/h. At the s...

The number of degrees of freedom in a planner mechanism having $$n$$ links and $$j$$ simple hinge joints is

In a certain slider-crank mechanism, lengths of crank and connecting rod are equal. If the crank rotates with a uniform angular speed of 14 rad/s and the crank length is 300 mm, th...

Consider an ant crawling along the curve $$\,{\left( {x - 2} \right)^2} + {y^2} = 4,$$ where $$x$$ and $$y$$ are in meters. The ant starts at the point $$(4, 0)$$ and moves counter...

A ball of mass 0.1 kg, initially at rest, is dropped from height of 1m. Ball hits the ground and bounces off the ground. Upon impact with the ground, the velocity reduces by 20%. T...

The initial velocity of an object is $$40$$ $$m/s.$$ The acceleration a of the object is given by the following expression: a$$=-0.1v$$ Where v is the instantaneous velocity of the...

For the given statements: ($$I.$$) $$\,\,\,$$ Mating spur gear teeth is an example of higher pair ($$II.$$) $$\,\,\,$$ A revolute joint is an example of lower pair. Indicate the co...

Consider the following statements regarding streamline(s): (i) It is a continuous line such that the tangent at any point on it shows the velocity vector at that point (ii) There i...

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

Consider a velocity field $$\overrightarrow V = K\left( {y\widehat i + x\widehat k} \right),$$ where $$K$$ is a constant. The vorticity, $${\Omega _z},$$ is

Mobility of a statically indeterminate structure is

Velocity vector of a flow fields is given as $$\overrightarrow V = 2xy\widehat i - {x^2}z\widehat j.$$ The vorticity vector at $$(1,1,1)$$ is

There are two points P and Q on a planar rigid body. The relative velocity between the two points

You are asked to evaluate assorted fluid flows for their suitability in a given laboratory application. The following three flow choices. Expressed in terms of the two - dimensiona...

Match the approaches given below to perform stated kinematics/dynamics analysis of machine Analysis $$P.$$ Continuous relative rotation $$Q.$$ Velocity and acceleration $$R.$$ Mobi...

A planar mechanism has 8 links and 10 rotary joints. The number of degrees of freedom of the mechanism, using Gruebler's criterion, is

A straight rod length $$L(t),$$ hinged at one end freely extensible at the other end, roates through an angle $$\theta \left( t \right)$$ about the hinge. At time $$t,$$ $$L(t)=1m,...

In a four-bar linkage, $$S$$ denotes the shortest link length, $$L$$ is the longest link length, $$P$$ and $$Q$$ are the lengths of other two links. At least one of the three movin...

A two-dimensional flow field has velocities along the $$x$$ and $$y$$ directions given by $$u = {x^2}t$$ and $$v = - 2xyt$$ respectively, where $$t$$ is time. The equation of strea...

For a four bar linkage in Toggle position, the value of mechanical advantage is

A leaf is caught in a whirlpool. At a given instant, the leaf is at a distance of $$120$$ $$m$$ from the centre of the whirlpool. The whirlpool can be described by the following ve...

The velocity components in the $$x$$ and $$y$$ directions of a two dimensional potential flow are $$u$$ and $$v$$, respectively. Then $${{\partial u} \over {\partial y}}$$ is equal...

A fluid flow is represented by the velocity field $$\overrightarrow V = ax\,\overrightarrow i + ay\,\overrightarrow j ,$$ where a constant . The equation of stream line passing thr...

The mechanism used in a shaping machine is

The lengths of the links of a 4-bar linkage with revolute pairs only are $$p,q,r$$ and $$s$$ units. Given that $$p < q < r < s.$$ Which of these links should be the fixed one, for...

A car moving with uniform acceleration covers 450 m in a 5 second interval, and covers 700 m in the next 5 second interval. The acceleration of the car is

Circulation is defined as line integral of tangential component of velocity about a _________ (fill in the blank)

A velocity field is given as $$$\overrightarrow V = 3{x^2}y\widehat i - 6xyz\widehat k$$$ Where $$x,y,z$$ are in $$m$$ and $$V$$ $$m/s.$$ Determine if (i) It represents an incompre...

Instantaneous centre of a body rolling with sliding on a stationary curved surface lies.

Instantaneous center of a body rolling with sliding on a stationary curved surface lies

The stream function in a two dimensional flow field is given by $$\Psi = {x^2} - {y^2}$$ The magnitude of the velocity at point $$(1,1)$$ is

A Newtonian fluid has the following velocity field : $$$\overrightarrow V = {x^2}y\widehat i + 2x{y^2}z\widehat j - y{z^3}\widehat k$$$ The rate of shear deformation $${\varepsilon...