List of top Mechanical Engineering Questions

The smallest perimeter that a rectangle with area of 4 square units can have is ............... units. (Answer in integer)

Consider the second-order linear ordinary differential equation \[ x^2 \frac{d^2y}{dx^2} + x \frac{dy}{dx} - y = 0, x \ge 1 \] with the initial conditions \[ y(x = 1) = 6, \frac{dy}{dx}\bigg|_{x=1} = 2. \] The value of y at x = 2 equals ................ (Answer in integer)

The initial value problem \[ \frac{dy}{dt} + 2y = 0, y(0) = 1 \] is solved numerically using the forward Euler's method with a constant and positive time step of \(\Delta t\). Let \(y_n\) represent the numerical solution obtained after n steps. The condition \(|y_{n+1}| \le |y_n|\) is satisfied if and only if \(\Delta t\) does not exceed ................ (Answer in integer)

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 linear transformation maps a point \((x, y)\) in the plane to the point \((\hat{x}, \hat{y})\) according to the rule \[ \hat{x} = 3y, \hat{y} = 2x. \] Then, the disc \(x^2 + y^2 \le 1\) gets transformed to a region with an area equal to ................ (Rounded off to two decimals)
Use \(\pi = 3.14\).

The value of k that makes the complex-valued function \[ f(z) = e^{-kx} (\cos 2y - i \sin 2y) \] analytic, where \(z = x + iy\), is ................ (Answer in integer)

The principal stresses at a point P in a solid are 70 MPa, -70 MPa and 0. The yield stress of the material is 100 MPa. Which prediction(s) about material failure at P is/are CORRECT?

Two surfaces P and Q are to be joined together. In which of the given joining operation(s), there is no melting of the two surfaces P and Q for creating the joint?

In a metal casting process to manufacture parts, both patterns and moulds provide shape by dictating where the material should or should not go. Which of the option(s) given correctly describe(s) the mould and the pattern?

Air (density = 1.2 kg/m³, kinematic viscosity = 1.5×10⁻⁵ m²/s) flows over a flat plate with a free-stream velocity of 2 m/s. The wall shear stress at a location 15 mm from the leading edge is \(\tau_w\). What is the wall shear stress at a location 30 mm from the leading edge?

Consider an isentropic flow of air (ratio of specific heats = 1.4) through a duct as shown in the figure. The variations in the flow across the cross-section are negligible. The flow conditions at Location 1 are given as follows:
\(P_1 = 100\) kPa, \(\rho_1 = 1.2\) kg/m³, \(u_1 = 400\) m/s
The duct cross-sectional area at Location 2 is given by \(A_2 = 2A_1\), where \(A_1\) denotes the duct cross-sectional area at Location 1. Which one of the given statements about the velocity \(u_2\) and pressure \(P_2\) at Location 2 is TRUE?

A machine produces a defective component with a probability of 0.015. The number of defective components in a packed box containing 200 components produced by the machine follows a Poisson distribution. The mean and the variance of the distribution are

What are the number of numbers possible divisible by 3 if we choose 4 numbers from the set S = {4,5,7,8,9}