#mu engineering
- A force 30 N is acting at point P(3, 2, 1) m. The force makes 35° & 85° with x & y axes respectively. Express the force in vector form. Direction cosines satisfy cos²θ_x + cos²θ_y + cos²θ_z = 1 : cos²θ_z = 1 - cos² 35^° - cos² 85^° = 1 - 0.6710 - 0.0076 = 0.3214 ⇒ cosθ_z = 0.... 1
- The acceleration of the particle is defined by the relation \(a = 25 - 3x^2\ \text{mm/s}^2\). The particle starts with no initial velocity at the position x = 0. Determine the position where the velocity is maximum and the corresponding maximum veloc… Using vdv/dx = a : displaystyle∫₀^v v dv = ∫₀^x (25 - 3x²) dx ⇒ v²/2 = 25x - x³ Maximum velocity when dv/dx = 0 , i.e. when a = 0 : 25 - 3x²... 1
- A cricket ball of mass 0.15 kg is moving with a velocity of 20 m/s. A player catches it and brings it to rest in 0.1 s. Find the impulse and average force applied. Impulse = change in momentum = m(v - u) = 0.15(0 - 20) = -3 N·s i.e. impulse of magnitude 3 N·s opposite to the ball's motion. Average force... 1
- Find the coordinate of the centroid for the shaded part of the lamina with respect to given reference axis.[Figure: origin O with x-axis to the right and y-axis upward. A semicircle of radius R = 8 cm (the digit is partly obscured in the scan; read a… Components (cm): triangle height h = 8tan60^° = 13.856 cm. PartA (cm²)x (cm)y (cm)AxAy 1 Semicircle R = 8 (below x-axis) π 8²/2 = 100.531 0... 1
- The motion of a particle is defined by the position vector, \(\bar r = 5t\,i + 3t^2\,j\) where ‘r’ is in meters and t is in seconds. At the instant when t = 2 sec, find i) Tangential and normal components of accelerations ii) Radius of curvature. bar v = 5 i + 6t j ; at t = 2 s: bar v = 5 i + 12 j , v = √(25 + 144) = 13 m/s bar a = 6 j m/s² (constant), a = 6 m/s² i) Tangential compone... 1
- A system of forces acting on a bell crank is as shown in fig. Determine the magnitude, direction and the point of application of the resultant w.r.t. O.[Figure: bell crank pivoted at O. A horizontal arm extends 300 mm to the left of O (two segments o… Axes: O origin, x right, y up; forces in N, distances in mm. ForcePoint (x, y) F_x F_y M_O = xF_y - yF_x 500 N(−300, 0)+250−433.01+129 904 1... 1
- In the mechanism shown in fig, the angular velocity of link AB is 5 rad/sec anticlockwise. At the instant shown, determine the angular velocity of link BC and velocity of piston C.[Figure: link AB hangs vertically from a fixed pivot A; AB = 200 mm, r… Velocity of B: v_B = ω_AB × AB = 5 × 0.2 = 1 m/s, perpendicular to AB. With B directly below A and AB rotating anticlockwise, v_B is horizon... 1
- Determine the force P applied at 30° to the horizontal just necessary to start a roller having 50 cm radius over a 12 cm high obstruction, if the roller is of 100 kg mass. Also find the magnitude and direction of P when it is minimum.[Figure: roller… Given: W = 100 × 9.81 = 981 N, r = 50 cm, h = 12 cm. When the roller is just about to climb, the floor reaction becomes zero; the forces are... 1
- The system shown in figure is initially at rest. Neglecting friction determine the force ‘P’ required if the velocity of the collar B is 5 m/s after 2 sec and corresponding tension in the cable.[Figure: a horizontal smooth rod is fixed to a vertical… Given: m_B = 3 kg, m_A = 1.5 kg, system starts from rest, v_B = 5 m/s after t = 2 s, all surfaces and pulleys frictionless. 1. Constraint (k... 1
- Find the force P required to pull block B shown in figure. Coefficient of friction between A and B is 0.3 and between B and floor is 0.25. Mass of A = 20 kg and B = 30 kg.[Figure: block B rests on a horizontal floor and block A rests on top of B. A s… Given: W_A = 20 × 9.81 = 196.2 N, W_B = 30 × 9.81 = 294.3 N, μ₁ = 0.3 (A–B), μ₂ = 0.25 (B–floor). A is held by the string; B is about to mov... 1
- A 3 kg mass kept on a 30° slope is subjected to a variable force \(P = (t^2 + 3)\), where P is in ‘Newton’ and t is in ‘second’ find velocity of the block after 5 second using Impulse momentum principle. At t = 0, V = 0.[Figure: block on an incline r… Given: m = 3 kg, W = 29.43 N, μ = 0.2 , P = t² + 3 N down the slope, u = 0. The block moves down the slope, so friction acts up the slope. N... 1
- For the beam loaded as shown in figure, Calculate the support reactions.[Figure: cantilever AB, 3 m long, fixed at A (left wall). A UDL of 10 kN/m acts over the first 2 m from A. At 2 m from A, a 20 kN force acts downward to the left, inclined at 60°… Loads: UDL resultant = 10 × 2 = 20 kN at 1 m from A. Inclined 20 kN: vertical component 20sin60^° = 17.32 kN (↓), horizontal component 20cos... 1
- A simple 2 DOF planar robot is shown. Prepare a D H parameter table and perform forward kinematics to find the location and orientation of end effector B.[Figure: base joint O on a fixed support. Link OA, 3 m long, makes 110° measured anticlockwise f… Joint angles: θ₁ = 110^° ; θ₂ = -65^° (measured clockwise from the extension of link 1). Link 2 absolute angle = θ₁ + θ₂ = 45^° . Link i θ_i... 1
- A sample of coal has the following composition C = 84 %, O = 8.4 %, H = 5.5 %, S = 1.5%, N = 0.6 %, Calculate the higher and lower calorific values of coal. Given: C = 84%, H = 5.5%, O = 8.4%, S = 1.5%, N = 0.6% (N does not contribute to the heat). Dulong's formula (C, H, O, S in %): HCV = 1/100[... 1
- Explain fiber reinforced composite and write its applications and limitations. Fibre-reinforced composites (FRC) are composites in which the dispersed phase is in the form of fibres, i.e. long, thin filaments with a hig... 1
- An alloy of Cd and Bi contain 25% of Cd Find the mass of eutectic in 1kg of solid Alloy, if the eutectic contains 40 % of Cd. Given: the alloy has 25% Cd (75% Bi), and the eutectic has 40% Cd (60% Bi). The alloy has less Cd (25%) than the eutectic (40%), so it has e... 1
- How material selection and proper design of equipments can prevent corrosion. Explain with the help of diagram and designing principles. 1. Proper selection of material Use noble or corrosion-resistant metals (Pt, Au, Ti) or alloys such as stainless steel and cupronickel where... 1
- What are advantages of gaseous fuels over solid and liquid fuels? They can be carried easily through pipelines to the point of use, so there is no handling or storage labour. They mix intimately with air, s... 1
- Distinguish between galvanizing and tinning. GalvanizingTinning Iron or steel is coated with zinc, usually by dipping in molten Zn at about 450 °C.Iron or steel is coated with tin, usua... 1
- Why are alloys preferred over pure metals in many applications? Pure metals are generally soft, ductile, of low strength, easily corroded and hard to cast. Alloying improves these properties, so alloys ar... 1
- Explain viscoelasticity property of polymer. Viscoelasticity is the property of polymers by which they show both elastic (solid-like) and viscous (liquid-like) behaviour when deformed.... 1
- Define Matrix phase and dispersed phase of composites. A composite has two constituents: 1. Matrix phase – the continuous phase that surrounds and binds the other phase. It may be a polymer, meta... 1
- What is supercritical CO2 and how does it differ from liquid and gaseous CO2. Supercritical CO₂ (scCO₂) is CO₂ held above its critical temperature (T_c = 31.1 °C) and critical pressure (P_c = 72.8 atm ≈ 7.38 MPa). Abov... 1
- 1 gm. of coal sample was used for determination of nitrogen. The ammonia evolved was passed into 50ml of 0.1 N H2SO4, the excess acid required 42 ml. of 0.1N NaOH for neutralization Calculate % of N. Given: W = 1 g; acid taken = 50 mL of 0.1 N H₂SO₄; excess acid = 42 mL of 0.1 N NaOH. Volume of 0.1 N acid used by NH₃ = 50 − 42 = 8 mL. %N... 1