Engineering Mechanics Static and Dynamics · Engineering Mechanics · GATE ME

A ram in the form of a rectangular body of size $l = 9 \text{ m}$ and $b = 2 \text{ m}$ is suspended by two parallel ropes of lengths $7 \text{ m}$. A...

A rigid massless tetrahedron is placed such that vertex O is at the origin and the other three vertices A, B, and C lie on the coordinate axes as show...

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

A massive uniform rigid circular disc is mounted on a frictionless bearing at the end E of a massive uniform rigid shaft AE which is suspended horizon...

Match the additive manufacturing technique in Column I with its corresponding input material in Column II. Additive manufacturing techni...

A square plate is supported in four different ways (configurations (P) to (S) as shown in the figure). A couple moment C is applied on the plate. Assu...

A rope with two mass-less platforms at its two ends passes over a fixed pulley as shown in the figure. Discs with narrow slots and having equal weight...

The plane of the figure represents a horizontal plane. A thin rigid rod at rest is pivoted without friction about a fixed vertical axis passing t...

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) = ...

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

A point mass having mass $$M$$ is moving with a velocity $$V$$ at an angle $$\mathop \theta \limits^ \cdot $$ to the wall as shown in the figure. The...

A force $$F$$ is acting on a bent bar which is clamped at one end as shown in the figure. The CORRECT free body diagram is ...

A rigid ball of weight $$100$$ $$N$$ is suspended with the help of a string. The ball is pulled by a horizontal force $$F$$ such that the string makes...

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 surf...

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 perfec...

Two identical trusses support a load of 100 N as shown in the figure. The length of each truss is 1.0m; cross-sectional area is 200 mm2 ; Young’s modu...

A weight of 500N is supported by two metallic ropes as shown in the figure. The values of tensions T1 and T2 are respectively. ...

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

A two member truss ABC is shown in the figure. The force (in kN) transmitted in member AB is ________ ...

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 co...

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. After the collision, both th...

The coefficient of restitution of a perfectly plastic impact is

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 rubber band as a function of dist...

A block weighing 981 $$N$$ is resting on a horizontal surface. The coefficient of friction between the block and the horizontal surface is $$\mu = 0....

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 hi...

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 ...

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' acceler...

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 is subjected to a load of v...

A truss consists of horizontal members (AC, CD, DB and EF) and vertical members (CE and DE) having length 1 each. The members AE, DE and BF are inclin...

A bullet of mass ‘m’ travels at a very high velocity v (as shown in the figure) and gets embedded inside the block of mass ‘M’ initially at rest on a ...

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 fo...

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

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 ca...

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...

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...

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 wh...

The cylinder shown below rolls without slipping. In which direction does the friction force act? Towards which of the following points is the acceler...

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

A and B are the end -points of a diameter of a disc rolling along a straight line with a counter Clock-wise angular velocity as shown in the figure. R...

A three-hinge arch ABC in the form of a semi-circle is shown in the figure. The arch is in static equilibrium under vertical loads of $P = 100$ kN and...

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 e...

A rigid homogeneous uniform block of mass 1 kg, height h = 0.4 m and width b = 0.3 m is pinned at one corner and placed upright in a uniform gravitati...

A rigid body in the X-Y plane consists of two point masses (1 kg each) attached to the ends of two massless rods, each of 1 cm length, as shown in the...

A rigid beam AD of length 3a = 6 m is hinged at frictionless pin joint A and supported by two strings as shown in the figure. String BC passes over tw...

The lengths of members BC and CE in the frame shown in the figure are equal. All the members are rigid and lightweight, and the friction at the joints...

A structure, along with the loads applied on it, is shown in the figure. Self-weight of all the members is negligible and all the pin joints are frict...

Two rigid massless rods PR and RQ are joined at frictionless pin-joint R and are resting on ground at P and Q, respectively, as shown in the figure. A...

A cylindrical disc of mass m = 1 kg and radius r = 0.15 m was spinning at 𝜔 = 5 rad/s when it was placed on a flat horizontal surface and releas...

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 slipp...

The rod PQ of length L = 2 m, and uniformly distributed mass of M = 10 kg, is released from rest at the position shown in the figure. The ends slide a...

A system of particles in motion has mass center $$G$$ as shown in the figure. The particle $$i$$ has mass $${m_i}$$ and its position with respect to a...

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 spe...

An inextensible massless string goes over a frictionless pulley. Two weights of 100 N and 200 N are attached to the two ends of the string. The weight...

A rigid rod $$(AB)$$ of length $$L = \sqrt 2 $$ m is undergoing translational as well as rotational motion in the $$ x-y$$ plane (see the figure). Th...

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 coefficient of static friction betwee...

A two-member truss $$PQR$$ is supporting a load W. The axial forces in members $$PQ$$ and $$QR$$ are respectively ...

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 ...

For the truss shown in the figure, the magnitude of the force (in kN) in the member SR is ...

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, ...

For the truss shown in figure, the magnitude of the force in member PR and the support reaction at R are respectively ...

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 ...

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 QS is ...

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 shown in the figure. The magni...

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 as shown in the figure. A forc...

A ladder AB of length 5 m and weight (W) 600 N is resting against a wall. Assuming frictionless contact at the floor (B) and the wall (A), the magnitu...

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. T...

A rigid link PQ of length 2 m rotates about the pinned end Q with a constant angular acceleration of 12 rad/s2 . When the angular velocity of the link...

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 massless and inextensible stri...

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 a...

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 rad...

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...

A body of mass (m) 10kg is initially stationary on a 45° inclined plane as shown in figure. The coefficient of dynamic friction between the body and t...

A pin jointed uniform rigid rod of weight W and length is supported horizontally by an external force F as shown in the figure below. The force F is s...

Two steel truss members, AC and BC, each having cross sectional area of 100 mm2, are subjected to a horizontal force F as shown in figure. All the joi...

Two steel truss members, AC and BC, each having cross sectional area of 100 mm2, are subjected to a horizontal force F as shown in figure. All the joi...

A 1 kg block is resting on a surface with coefficient of friction $$\mu $$ $$=0.1.$$ A force of $$0.8$$ $$N$$ is applied to the block as shown in the ...

A uniform rigid rod of mass $$M$$ and length $$L$$ is hinged at one end as shown in theadjacent figure. A force P is applied at a distance of $$2L/3$$...

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

Consider a truss $$PQR$$ loaded at $$P$$ with a force $$F$$ as shown in the figure. The tension in the member $$QR$$ is ...

A block of mass $$M$$ is related from point $$P$$ on a rough inclined plane with inclination angle $$\theta $$, shown in the figure below. The coeffic...

If point A is in equilibrium under the action of the applied forces, the values of tensions and T AB and TAC are respectively. ...

A shell is fired from a cannon. At the instant the shell is just about to leave the barrel, its velocity relative to the barrel is 3m/s, while the bar...

An elevator (lift) consists of the elevator cage and a counter weight, of mass m each. The cage and the counterweight are connected by a chain that pa...

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 lowe...

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 a mass of 20 kg and a radius o...

The figure below shown a pair of pin jointed gripper tongs holding an object weighing $$2000N$$. The coefficient of friction (µ) at the gripping surfa...

A rigid body shown in the fig.(a) has a mass of 10kg. It rotates with a uniform angular velocity $$'\omega '$$ A balancing mass of 20 kg is attached...

An ejector mechanism consists of a helical compression spring having a spring constant of k = 981 × 103 N/m. It is pre-compressed by 100mm from its fr...

A reel of mass $$'‘m'’$$ and radius of gyration $$'‘'k’$$ is rolling down smoothly from rest with one end of the thread wound on it held in the ceilin...

A reel of mass $$'‘m'’$$ and radius of gyration $$'‘'k’$$ is rolling down smoothly from rest with one end of the thread wound on it held in the ceilin...

A shown in Figure, a person A is standing at he centre of a rotating platform facing person B who is riding a bicycle, heading East. The relevant spee...

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 pin reactions at A on the bar A...

Match 4 correct pairs between List $$I$$ and List $$II$$. No credit will be given for partially correct matching List $$I$$ (a) Collision of particle...

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 horizontal plane, the velocity...

AB and CD tow uniform and identical bars of mass 10kg each, as shown. The hinges at A and B are frictionless. The assembly is released from rest and m...

A spring scale indicates a tension $$T$$ in the right hand cable of the pulley system shown in figure below. Neglecting the mass of the pulleys and ig...