GATE ME

Engineering Mechanics Static and Dynamics

Engineering Mechanics

(Past Years Questions)

Marks 1

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A Particle of unit mass is moving on a plane. Its trajectory, in polar coordinates, is given by $$r\left( t \right) = {t...
GATE ME 2017 Set 1
The following figure shows the velocity- time plot for a particle traveling along a straight line. The distance covered ...
GATE ME 2017 Set 1
A force $$F$$ is acting on a bent bar which is clamped at one end as shown in the figure. The CORRECT free body diag...
GATE ME 2016 Set 3
A point mass having mass $$M$$ is moving with a velocity $$V$$ at an angle $$\mathop \theta \limits^ \cdot $$ to the w...
GATE ME 2016 Set 2
A rigid ball of weight $$100$$ $$N$$ is suspended with the help of a string. The ball is pulled by a horizontal force $$...
GATE ME 2016 Set 1
A point mass $$M$$ is released from rest and slides down a spherical bowl (of radius $$R$$) from a height $$H$$ as shown...
GATE ME 2016 Set 1
A weight of 500N is supported by two metallic ropes as shown in the figure. The values of tensions T1 and T2 are respect...
GATE ME 2015 Set 3
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 m...
GATE ME 2015 Set 2
Two identical trusses support a load of 100 N as shown in the figure. The length of each truss is 1.0m; cross-sectional ...
GATE ME 2015 Set 1
In a statically determinate plane truss, the number of joints $$(j)$$ and the number of members $$(m)$$ are related by...
GATE ME 2014 Set 4
A mass m1 of 100kg travelling with a uniform velocity of 5 m/s along a line collides with a stationary mass m2 of 1000kg...
GATE ME 2014 Set 3
A two member truss ABC is shown in the figure. The force (in kN) transmitted in member AB is ________ ...
GATE ME 2014 Set 2
A circular object of radius r rolls without slipping on a horizontal level floor with the center having velocity $$V$. T...
GATE ME 2014 Set 1
The coefficient of restitution of a perfectly plastic impact is
GATE ME 2011
A stone with mass of $$0.1$$kg is catapulted as shown in the figure. The total force $${F_x}$$ (in N) exerted by the rub...
GATE ME 2011
A block weighing 981 $$N$$ is resting on a horizontal surface. The coefficient of friction between the block and the hor...
GATE ME 2009
A straight rod length $$L(t),$$ hinged at one end freely extensible at the other end, roates through an angle $$\theta \...
GATE ME 2008
During inelastic collision of two particles, which one of the following is conserved?
GATE ME 2007
The time variation of the position of a particle in rectilinear motion is given by $$x = 2{t^3} + {t^2} + 2t$$. If 'V' i...
GATE ME 2005
A simple pendulum of length 5m, with a bob of mass 1 kg, is in simple harmonic motion. As it passes through its mean pos...
GATE ME 2005
The figure shows a pin-jointed plane truss loaded at the point M by hanging a mass of 100 kg. The member LN of the truss...
GATE ME 2004
A truss consists of horizontal members (AC, CD, DB and EF) and vertical members (CE and DE) having length 1 each. The me...
GATE ME 2003
A bullet of mass ‘m’ travels at a very high velocity v (as shown in the figure) and gets embedded inside the block of ma...
GATE ME 2003
A steel wheel of 600 mm diameter rolls on a horizontal steel rail. It carries a load of 500 N. The coefficient of rollin...
GATE ME 2000
The ratio of tension on the tight side to that on the slack side in a flat belt drive is
GATE ME 2000
A car moving with uniform acceleration covers 450 m in a 5 second interval, and covers 700 m in the next 5 second interv...
GATE ME 1998
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...
GATE ME 1996
A wheel of mass m and radius r is in accelerated rolling motion without slip under a steady axial torque $$T$$. If the c...
GATE ME 1996
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 i...
GATE ME 1994
The cylinder shown below rolls without slipping. In which direction does the friction force act? Towards which of the f...
GATE ME 1993
Instantaneous centre of a body rolling with sliding on a stationary curved surface lies.
GATE ME 1992
A and B are the end -points of a diameter of a disc rolling along a straight line with a counter Clock-wise angular velo...
GATE ME 1990

Marks 2

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The rod PQ of length L = 2 m, and uniformly distributed mass of M = 10 kg, is released from rest at the position shown i...
GATE ME 2017 Set 2
Two disks A and B with identical mass (m) and radius (R) are initially at rest. They roll down from the top of identical...
GATE ME 2017 Set 1
An inextensible massless string goes over a frictionless pulley. Two weights of 100 N and 200 N are attached to the two ...
GATE ME 2016 Set 3
A circular disc of radius 100 mm and mass 1 kg, initially at rest at position A, rolls without slipping down a curved pa...
GATE ME 2016 Set 3
A rigid rod $$(AB)$$ of length $$L = \sqrt 2 $$ m is undergoing translational as well as rotational motion in the $$ x-...
GATE ME 2016 Set 3
A system of particles in motion has mass center $$G$$ as shown in the figure. The particle $$i$$ has mass $${m_i}$$ and ...
GATE ME 2016 Set 2
A block of mass m rests on an inclined plane and is attached by a string to the wall as shown in the figure. The coeffic...
GATE ME 2016 Set 1
A two-member truss $$PQR$$ is supporting a load W. The axial forces in members $$PQ$$ and $$QR$$ are respectively ...
GATE ME 2016 Set 1
A bullet spins as the shot is fired from a gun. For this purpose, two helical slots as shown in the figure are cut in th...
GATE ME 2015 Set 3
The initial velocity of an object is $$40$$ $$m/s.$$ The acceleration a of the object is given by the following expressi...
GATE ME 2015 Set 2
For the truss shown in the figure, the magnitude of the force (in kN) in the member SR is ...
GATE ME 2015 Set 2
For the truss shown in figure, the magnitude of the force in member PR and the support reaction at R are respectively ...
GATE ME 2015 Set 1
A ball of mass 0.1 kg, initially at rest, is dropped from height of 1m. Ball hits the ground and bounces off the ground....
GATE ME 2015 Set 1
For the truss shown in the figure, the forces F1 and F2 are 9 kN and 3 kN, respectively. The force (in kN) in the member...
GATE ME 2014 Set 4
A uniform slender rod (8 m length and 3 kg mass) rotates in a vertical plane about a horizontal axis 1m from its end as ...
GATE ME 2014 Set 4
A wardrobe (mass 100 kg, height 4 m, width 2 m, depth 1 m), symmetric about the Y-Y axis, stands on a rough level floor ...
GATE ME 2014 Set 4
A ladder AB of length 5 m and weight (W) 600 N is resting against a wall. Assuming frictionless contact at the floor (B)...
GATE ME 2014 Set 4
A body of mass (m) 10kg is initially stationary on a 45° inclined plane as shown in figure. The coefficient of dynamic f...
GATE ME 2014 Set 3
An annular disc has a mass m, inner radius R and outer radius $$2R$$. The disc rolls on a flat surface without slipping....
GATE ME 2014 Set 3
A four-wheel vehicle of mass 1000kg moves uniformly in a straight line with the wheels revolving at 10 rad/s. The wheel ...
GATE ME 2014 Set 3
A truck accelerates up a 10° incline with a crate of 100 kg. Value of static coefficient of friction between the crate a...
GATE ME 2014 Set 2
A block R of mass 100 kg is placed on a block S of mass 150 kg as shown in the figure. Block R is tied to the wall by a ...
GATE ME 2014 Set 1
A block weighing 200N is in contact with a level plane whose coefficients of static and kinetic friction are 0.4 and 0.2...
GATE ME 2014 Set 1
A rigid link PQ of length 2 m rotates about the pinned end Q with a constant angular acceleration of 12 rad/s2 . When th...
GATE ME 2014 Set 1
A pin jointed uniform rigid rod of weight W and length is supported horizontally by an external force F as shown in the ...
GATE ME 2013
Two steel truss members, AC and BC, each having cross sectional area of 100 mm2, are subjected to a horizontal force F a...
GATE ME 2012
Two steel truss members, AC and BC, each having cross sectional area of 100 mm2, are subjected to a horizontal force F a...
GATE ME 2012
A 1 kg block is resting on a surface with coefficient of friction $$\mu $$ $$=0.1.$$ A force of $$0.8$$ $$N$$ is applied...
GATE ME 2011
A uniform rigid rod of mass $$M$$ and length $$L$$ is hinged at one end as shown in theadjacent figure. A force P is app...
GATE ME 2009
A circular disk of radius $$'R'$$ rolls without slipping at a velocity $$v$$. The magnitude of the velocity at point $$'...
GATE ME 2008
Consider a truss $$PQR$$ loaded at $$P$$ with a force $$F$$ as shown in the figure. The tension in the member $$QR$$ is ...
GATE ME 2008
A block of mass $$M$$ is related from point $$P$$ on a rough inclined plane with inclination angle $$\theta $$, shown in...
GATE ME 2007
If point A is in equilibrium under the action of the applied forces, the values of tensions and T AB and TAC are respec...
GATE ME 2006
A shell is fired from a cannon. At the instant the shell is just about to leave the barrel, its velocity relative to the...
GATE ME 2005
An elevator (lift) consists of the elevator cage and a counter weight, of mass m each. The cage and the counterweight ar...
GATE ME 2005
Two books of mass 1 kg each are kept on a table, one over the other. The coefficient of friction on every pair of contac...
GATE ME 2005
A 1 kg mass of clay, moving with a velocity of 10 m/s, strikes a stationary wheel and sticks to it. The solid wheel has ...
GATE ME 2005
The figure below shown a pair of pin jointed gripper tongs holding an object weighing $$2000N$$. The coefficient of fric...
GATE ME 2004
An ejector mechanism consists of a helical compression spring having a spring constant of k = 981 × 103 N/m. It is pre-c...
GATE ME 2004
A rigid body shown in the fig.(a) has a mass of 10kg. It rotates with a uniform angular velocity $$'\omega '$$ A balan...
GATE ME 2004
A reel of mass $$'‘m'’$$ and radius of gyration $$'‘'k’$$ is rolling down smoothly from rest with one end of the thread ...
GATE ME 2003
A reel of mass $$'‘m'’$$ and radius of gyration $$'‘'k’$$ is rolling down smoothly from rest with one end of the thread ...
GATE ME 2003
A shown in Figure, a person A is standing at he centre of a rotating platform facing person B who is riding a bicycle, h...
GATE ME 1999
A mass of 35 kg is suspended from a weightless bar AB which is supported by a cable CB and a pin at A as shown in. The p...
GATE ME 1997
AB and CD tow uniform and identical bars of mass 10kg each, as shown. The hinges at A and B are frictionless. The assemb...
GATE ME 1996
A rod of length 1m is sliding in a corner as shown in. At an instant when the rod makes an angle of 60 degrees with the ...
GATE ME 1996
Match 4 correct pairs between List $$I$$ and List $$II$$. No credit will be given for partially correct matching List $...
GATE ME 1996
A spring scale indicates a tension $$T$$ in the right hand cable of the pulley system shown in figure below. Neglecting ...
GATE ME 1995

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