#mu engineering
- Explain the working principle and transformation ratio of a single-phase transformer. Principle: mutual induction (Faraday's law). When an alternating voltage is applied to one winding, the alternating flux it produces links t... 1
- Find current flowing through 1 Ω resistance by Node analysis. [Circuit: a common bottom wire (reference). Left vertical branch: a 4 V battery from the bottom wire up to the left node L (longer plate, +, at the top). From L the left vertical wire cont… Reference: bottom wire = 0 V. Node voltages: V_L, V_M, V_R. The 4 V source is directly between L and reference ⇒ V_L = 4 V. KCL at node R (c... 1
- Write short note on any one: (i) Single phase induction motor (ii) BLDC motor. (Answering option (ii); a note on (i) is also given briefly.) Brushless DC (BLDC) motor: a DC-supplied motor in which mechanical commutator... 1
- State the necessary condition for resonance in a series circuit. Compare series and parallel resonance. Condition for series resonance: in an R-L-C series circuit, resonance occurs when the inductive reactance equals the capacitive reactance, X... 1
- Write a short note on FET. Field Effect Transistor (FET): a three-terminal, unipolar (only majority carriers), voltage-controlled semiconductor device in which the cur... 1
- Write formulas for Delta to Star and Star to Delta transformation. Let the delta resistances be R₁₂, R₂₃, R₃₁ (between terminals 1-2, 2-3, 3-1) and the equivalent star resistances be R₁, R₂, R₃ (connected fr... 1
- Resolve the force F = 900 N acting at B as shown in Fig. into parallel components at O and A.[Figure: horizontal bar OAB; O at the left end, A at 1 m from O, B at the right end, 2 m from A (OB = 3 m). A vertical downward force of 900 N acts at B.] Given: 900 N ( downarrow ) at B; OA = 1 m, AB = 2 m, OB = 3 m. Let the parallel (vertical) components be F_O at O and F_A at A, both assumed... 1
- Determine the tensions in the cords AB and BC for equilibrium of 30 kg block.[Figure: a 30 kg block hangs vertically from joint B. Cord BA goes up to the left to a support A and makes 30° with the horizontal at B; cord BC goes up to the right to a su… Given: W = 30 × 9.81 = 294.3 N. At joint B three concurrent forces act: T_AB (30° above horizontal, to the left), T_BC (40° above horizontal... 1
- A support block is acted upon by two forces as shown in fig. Knowing that the coefficient of friction between the block & the incline are \(\mu_s = 0.35\), \(\mu_k = 0.25\). Determine the force P required to prevent it from slipping down.[Figure: a b… Given: W = 800 N (vertical), P horizontal (towards the uphill side), θ = 25^° , μ_s = 0.35 (impending motion, so static coefficient is used)... 1
- A force of magnitude 50 kN is acting at point A(2,3,4) m towards point B(6,−2,−3) m. Find the components of this force along X, Y and Z axis. Position vector: AB = (6-2)hat i + (-2-3)hat j + (-3-4)hat k = 4hat i - 5hat j - 7hat k m |AB| = √(16 + 25 + 49) = √(90) = 9.487 m Unit vect... 1
- The acceleration of a particle in rectilinear motion is given by \(a = 100 - 3x^2\ \text{m/s}^2\). Knowing that at t = 0, v = 0 and x = 0 find the velocity of the particle at x = 8 m. Since a is a function of x, use a = vdv/dx : v dv = (100 - 3x²) dx ⇒ displaystyle∫₀^v v dv = ∫₀^x (100 - 3x²) dx v²/2 = 100x - x³ At x = 8 m... 1
- Explain with neat sketch 1) Direct central Impact 2) Oblique central Impact. Line of impact: the common normal to the surfaces of the two colliding bodies at the point of contact. If the mass centres of both bodies li... 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. Points: B(3,0) on the X-axis, A(0,3) on the Y-axis, C(−3,0) on the negative X-axi… Split the shaded area (all dimensions in cm, r = 3 ): (1) square OCDA (+), (2) quarter circle centred at O in the first quadrant (+), (3) qu... 1
- The position vector of a particle which moves in the X-Y plane is given by \(\bar r = (3t^3 - 4t^2)\,i + (0.5t^4)\,j\) m. Calculate Velocity and acceleration at t = 4 Sec. Velocity: bar v = dbar r/dt = (9t² - 8t) i + 2t³ j At t = 4 s: bar v = (144 - 32) i + 128 j = 112 i + 128 j m/s |v| = √(112² + 128²) = √(289... 1
- Determine the resultant of the following force system as shown in figure. Also locate its position w.r.t. O. Radius of circle is 2 m.[Figure: circle of radius 2 m, centre O, with horizontal and vertical centre lines. Four horizontal forces act at poi… Coordinates of points (O origin, x right, y up, r = 2 m): 150 N at (-2cos60^°, 2sin60^°) = (-1, 1.732) ; 90 N at (1.732, 1) ; 200 N at (1.73... 1
- Collar B moves up with constant velocity of \(V_B = 2\) m/s. Rod AB is pinned at B. Find the angular velocity of rod AB and velocity of A.[Figure: collar B slides on a fixed vertical rod. Rod AB of length 1.5 m runs from B down to the left to end A;… Given: v_B = 2 m/s ↑, AB = 1.5 m at 50° to horizontal, A moves along a 30° incline. Relative velocity: vec v_B = vec v_A + vecω × vec r_(B/A... 1
- Determine the force P to cause the motion to impend. Take masses of the block A & B as 8 kg & 4 kg respectively and the coefficient of sliding friction as 0.3. The force P and the rope are parallel to the inclined plane. Assume frictionless pulley.[F… Given: m_A = 8 kg ( W_A = 78.48 N), m_B = 4 kg ( W_B = 39.24 N), μ = 0.3 , θ = 30^° . When P pulls A down the plane, the rope pulls B up the... 1
- Two spheres A and B weight 1000 N and 750 N. Determine the reaction at all contact points 1, 2, 3 and 4. \(r_A = 400\) mm, \(r_B = 300\) mm.[Figure: a container with a vertical wall on the left, a horizontal floor, and a right wall inclined at 60° to… Assumption (from the sketch): the lower sphere is B (r = 300 mm, 750 N) and the upper sphere is A (r = 400 mm, 1000 N). Contact points: 1 =... 1
- A 50 kg crate shown in fig. rest on horizontal plane for which the coefficient of kinetic friction is μ = 0.3. If the crate does not tip over when it is subjected to a 400 N force, determine the velocity of the crate in 8 sec starting from rest using… Given: m = 50 kg, W = 490.5 N, P = 400 N at 30°, μ_k = 0.3 , u = 0, t = 8 s. Normal reaction ( Σ F_y = 0 ): N = 490.5 - 400sin30^° = 290.5 N... 1
- A planar elbow manipulator is shown. Write the D H parameters and hence locate the position and orientation of the end E of the manipulator. Given \(L_1 = L_2 = 250\) mm and \(\theta_1 = \theta_2 = 30^\circ\).[Figure: base frame \(X_0, Y_0\) at O. Li… DH parameter table (both joints revolute, all joint axes parallel to Z, so d_i = 0 , α_i = 0 ): Link i θ_i d_i a_i α_i 1 θ₁ = 30^° 0 L₁ = 25... 1
- For the beam loaded as shown in figure, Calculate the support reactions at A and B.[Figure: beam AF, 9 m long. A (left end) is a hinge support; B is a roller support 6 m from A. Dimensions from A: 2 m (point of 40 kN load and 20 kN·m couple), 1 m to… Note: the magnitude of P is not printed in the paper, so the reactions are obtained in terms of P (substitute the value of P if supplied). T... 1
- A car is made to move by applying resultant force R = 2000 N along the x-axis. This resultant is developed due to two pulling forces \(F_1\) and \(F_2\) on two ropes as shown in figure. Determine the tension in individual ropes.[Figure: car with fron… Method: F₁ , F₂ and R form a force triangle (triangle law); apply the sine rule. The angle opposite R = 180° − 35° − 25° = 120°, so sin 120^... 1
- For the member shown in figure find the magnitude and direction of the resultant reaction at the hinged support A.[Figure: L-shaped member BAC. A is a hinge at the corner. AB is vertical, 3 m long, with its upper end B attached by a horizontal link t… The link at B can only exert a horizontal force R_B . Hinge A gives H_A and V_A . Σ M_A = 0:\ R_B × 3 = 30 × 4 ⇒ R_B = 40 N (acting to the l... 1
- Prove that angle of friction is equal to angle of repose. Angle of friction ( φ ): the angle between the resultant of the limiting friction F and the normal reaction N, and the normal reaction: tanφ... 1