List of top Mechanical Engineering Questions on Engineering Mechanics asked in GATE ME

The figure shows a block of mass \(m = 20\) kg attached to a pair of identical linear springs, each having a spring constant \(k = 1000\) N/m. The block oscillates on a frictionless horizontal surface. Assuming free vibrations, the time taken by the block to complete ten oscillations is ............... seconds. (Rounded off to two decimal places) Take \(\pi = 3.14\). 

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 floor. What is the angular velocity \(\omega_2\) of the bar PQ? 

Two meshing spur gears 1 and 2 with diametral pitch of 8 teeth per mm and an angular velocity ratio \(|\omega_2|/|\omega_1| = 1/4\), have their centers 30 mm apart. The number of teeth on the driver (gear 1) is ................ (Answer in integer) 

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

 

Which one of the options given represents the feasible region of the linear programming model: 
Maximize \(45X_1 + 60X_2\) 
\(X_1 \le 45\) 
\(X_2 \le 50\) 
\(10X_1 + 10X_2 \ge 600\) 
\(25X_1 + 5X_2 \le 750\) 

 

With reference to the Economic Order Quantity (EOQ) model, which one of the options given is correct? 

 

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 vector of the ball (in kg m/s) just after impact?
Take the acceleration due to gravity to be \(g = 9.8\) m/s². Options have been rounded off to one decimal place.
The braking system shown in the figure uses a belt to slow down a pulley rotating in the clockwise direction by the application of a force P. The belt wraps around the pulley over an angle \(\alpha = 270\) degrees. The coefficient of friction between the belt and the pulley is 0.3. The influence of centrifugal forces on the belt is negligible. During braking, the ratio of the tensions \(T_1\) to \(T_2\) in the belt is equal to ................ (Rounded off to two decimal places)
Take \(\pi = 3.14\).
Which one of the options given is the inverse Laplace transform of \(\frac{1}{s^3 - s}\)?
\(u(t)\) denotes the unit-step function.

A short shoe drum (radius 260 mm) brake is shown in the figure. A force of 1 kN is applied to the lever. The coefficient of friction is 0.4. 

The magnitude of the torque applied by the brake is _________ N.m (round off to one decimal place).

Two smooth identical spheres each of radius 125 mm and weight 100 N rest in a horizontal channel having vertical walls. The distance between vertical walls of the channel is 400 mm. 

The reaction at the point of contact between two spheres is _________ N (round off to one decimal place).

Consider a two-degree-of-freedom system as shown in the figure, where PQ is a rigid uniform rod of length \( b \) and mass \( m \). \[ \text{Assume that the spring deflects only horizontally and force } F \text{ is applied horizontally at Q. For this system, the Lagrangian, } L \text{ is} \]

An orthogonal cutting operation is performed using a single point cutting tool with a rake angle of 12° on a lathe. During turning, the cutting force and the friction force are 1000 N and 600 N, respectively. If the chip thickness and the uncut chip thickness during turning are 1.5 mm and 0.75 mm, respectively, then the shear force is ______ N (round off to one decimal place).