Dynamics

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 $30 \mathrm{~km} / \mathrm{h}$. Car P travels...

The velocity field of a certain two-dimensional flow is given by V(𝑥, 𝑦) = 𝑘(𝑥𝑖̂ − 𝑦𝑗̂) where 𝑘 = 2 s -1 . The coordinates 𝑥 and 𝑦 are in meters. Assume gravitational effects to be negligible. If the density of...

The steady velocity field in an inviscid fluid of density 1.5 is given to be $\vec{V}=(y^2-x^2)\hat{i}+(2xy)\hat{j} $ . Neglecting body forces, the pressure gradient at (x =1, y = 1) is ______.

Consider steady, one-dimensional compressible flow of a gas in a pipe of diameter 1 m. At one location in the pipe, the density and velocity are 1 kg/m 3 and 100 m/s, respectively. At a downstream location in the pipe, t...

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 same speed, it takes 14 seconds to pass a...

Two disks A and B with identical mass (m) and radius (R) are initially 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...

A Particle of unit mass is moving on a plane. Its trajectory, in polar coordinates, is given by $$r\left( t \right) = {t^2},\theta \left( t \right) = t,$$ where $$t$$ is time. The kinetic energy of the particle at time $...

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%. The height (in m) to which the ball will...

Within a boundary layer for a steady incompressible flow, the Bernoulli equation

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 object. The velocity of the object afte...

Couette flow is characterized by

A small ball of mass 1 kg moving with a velocity of 12 m/s undergoes a direct central impact with a stationary ball of mass 2 kg. The impact is perfectly elastic. The speed (in m/s) of 2 kg mass ball after the impact wil...

For the same material and the mass, which of the following configurations of flywheel will have maximum mass moment of inertia about the axis of rotation $$OO’$$ passing through the center of gravity

An ideal water jet with volume flow rate of $$0.05{m^3}/s$$ strikes a flat plane placed normal to its path and exerts a force of $$1000N.$$ Considering the density of water as $$1000$$ $$kg/{m^3},$$ the diameter (in $$mm...

A rigid link PQ of length 2 m rotates about the pinned end Q with a constant angular acceleration of 12 rad/s 2 . When the angular velocity of the link is 4 rad/s, the magnitude of the resultant acceleration (in m/s 2 )...

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

A block weighing 200N is in contact with a level plane whose coefficients of static and kinetic friction are 0.4 and 0.2, respectively. The block is acted upon by a horizontal force (in newton) P=10t, where t denotes the...

Consider a flywheel whose mass $$M$$ is distributed almost equally between a heavy, ring-like rim of radius $$R$$ and a concentric disk-like feature of radius $$R/2$$. Other parts of the flywheel, such as spokes, etc, ha...

A truck accelerates up a 10° incline with a crate of 100 kg. Value of static coefficient of friction between the crate and the truck surface is 0.3. The maximum value of acceleration (in m/s 2 ) of the truck such that th...

A four-wheel vehicle of mass 1000kg moves uniformly in a straight line with the wheels revolving at 10 rad/s. The wheel are identical, each with a radius of 0.2 m. Then a constant braking torque is applied to all the whe...

A mass m 1 of 100kg travelling with a uniform velocity of 5 m/s along a line collides with a stationary mass m 2 of 1000kg. After the collision, both the masses travel together with the same velocity. The coefficient of...

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

Water is coming out from a tap and falls vertically downwards. At the tap opening, the stream diameter is $$20$$ $$mm$$ with uniform velocity of $$2$$ $$m/s.$$ Acceleration due to gravity is $$9.81$$ $$m/{s^2}.$$ Assumin...

The coefficient of restitution of a perfectly plastic impact is

A smooth pipe of diameter $$200$$ $$mm$$ carries water. The pressure in the pipe at section $${S_1}\,\,$$ (elevation : $$10$$ $$m$$ ) is the $$50$$ $$kPa.$$ At section $${S_2}\,\,$$ (elevation : $$12$$ $$m$$ ) the pressu...

Consider steady, incompressible and irrotational flow through a reducer in a horizontal pipe where the diameter is reduced from $$20cm$$ to $$10cm.$$ The pressure in the $$20cm$$ pipe just upstream of the reducer is $$15...

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 $$t,$$ $$L(t)=1m,$$ $$L(t)=1m/s,$$ $$\theta \left( t \rig...

Which combination of the following statements about steady incompressible forced vortex flow is correct? P: Shear stress is zero at all points in the flow. Q: Velocity is directly proportional to the radius from the cent...

During inelastic collision of two particles, which one of the following is conserved?

A simple pendulum of length 5m, with a bob of mass 1 kg, is in simple harmonic motion. As it passes through its mean position, the bob has a speed of 5m/s. the net force on the bob at the mean position is

The time variation of the position of a particle in rectilinear motion is given by $$x = 2{t^3} + {t^2} + 2t$$. If 'V' is the velocity and 'a' acceleration of the particle in consistent units, the motion started with

A water container is kept on a weighing balance. Water from a tap is falling vertically into the container with a volume flow rate of $$'Q'$$; the velocity of the water when it hits the water surface is $$'U'$$. At a par...

Navier Stoke's equation represents the conservation of

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

Match 4 correct pairs between List $$I$$ and List $$II$$ . No credit will be given for partially correct matching List $$I$$ (a) Collision of particles (b) Stability (C) Satellite motion (D) Spinning top List $$II$$ (1)...

A wheel of mass m and radius r is in accelerated rolling motion without slip under a steady axial torque $$T$$. If the coefficient of kinetic friction is $$\mu $$, the friction force from the ground on the wheel is

A ball A of mass m falls under gravity from a height h and strikes another ball B of mass m which supported at rest on a spring of stiffness k. Assume perfectly elastic impact. Immediately after the impact

A stone of mass m at the end of a string of length l is whirled in a vertical circle at a constant speed. The tension in the string will be maximum when the stone is