GATE Mechanical Engineering

The options show frames consisting of rigid bars connected by pin joints. Which one of the frames is non-rigid?

Match the additive manufacturing technique in Column I with its corresponding input material in Column II. Additive manufacturing technique (Column I) Input Material (Column II) P....

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 mas...

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...

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...

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...

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 accelerati...

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 forc...

In a statically determinate plane truss, the number of joints $$(j)$$ and the number of members $$(m)$$ are related by

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 t...

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...

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...

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 wit...

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...

The coefficient of restitution of a perfectly plastic impact 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,...

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...

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 consi...

Two books of mass 1 kg each are kept on a table, one over the other. The coefficient of friction on every pair of contacting surfaces is 0.3. the lower book is pulled with a horizo...

The ratio of tension on the tight side to that on the slack side in a flat belt drive is

A steel wheel of 600 mm diameter rolls on a horizontal steel rail. It carries a load of 500 N. The coefficient of rolling resistance is 0.3 mm. The force in N, necessary to roll th...

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...

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. Imm...

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 for...

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

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