University of Mumbai first-year engineering Semester I Engineering Mechanics paper, June 2025 (KT), NEP 2020 scheme, with step-by-step solutions written with AI help and checked.
Mumbai University FE Sem 1 Engineering Mechanics (ESC101) Question Paper June 2025 (KT)
Written semester papers (NEP 2020 scheme): 60 marks and 2 hours for most first-year courses. Question 1 is compulsory, then any three of questions 2 to 6.
Sections
| Q.1 Solve any five (compulsory) | 6 questions | |
| Q.2 (attempt any three of Q.2 to Q.6) | 2 questions | |
| Q.3 | 2 questions | |
| Q.4 | 2 questions | |
| Q.5 | 2 questions | |
| Q.6 | 2 questions |
Chapters covered
Instructions
Solve on paper with a timer, then check against the solutions.
Q.1 Solve any five (compulsory)
-
Q.1 (a) 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.]
-
Q.1 (b) 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 support C and makes 40° with the horizontal at B.]
-
Q.1 (c) 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 block rests on an incline that slopes downward to the right at 25° to the horizontal. A vertical load of 800 N acts downward on the block, and a horizontal force P acts on the block pointing to the left (i.e. pushing the block towards the uphill side / into the incline).]
-
Q.1 (d) 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.
-
Q.1 (e) 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.
-
Q.1 (f) Explain with neat sketch 1) Direct central Impact 2) Oblique central Impact.
Q.2 (attempt any three of Q.2 to Q.6)
-
Q.2 (A) 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-axis, D(−3,3). Arc AB is a quarter circle centred at O with R = 3 cm. Arc CA is a quarter circle centred at D with R = 3 cm (concave towards D). The shaded region is bounded by OB, the arc BA, the arc AC and the line CO, i.e. the quarter circle OAB together with the part of square OCDA lying outside the quarter circle centred at D. Dimensions in cm.]
-
Q.2 (B) 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.
Q.3
-
Q.3 (A) 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 points on the circumference: 150 N pointing left at the point on the radius inclined at 60° above the horizontal on the left side (upper-left); 90 N pointing left (acting into the circle) at the point on the radius 30° above the horizontal on the right side (upper-right); 200 N pointing right at the point on the radius 30° below the horizontal on the right side (lower-right); 100 N pointing left at the point on the radius 45° below the horizontal on the left side (lower-left).]
-
Q.3 (B) 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; at B the rod makes 50° with the horizontal. End A slides on an inclined surface rising to the right at 30° to the horizontal (the incline then meets the horizontal ground on which the vertical rod stands).]
Q.4
-
Q.4 (A) 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 the horizontal (rising to the right). The lower, smaller sphere rests on the floor against the left wall; the upper, larger sphere rests on the lower sphere and against the inclined wall. The horizontal distance from the left wall to the vertical line through the centre of the upper sphere is 700 mm. The contact points are not individually labelled in the scan.]
-
Q.4 (B) 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 wall on the left. Collar B (mass 3 kg) slides on this rod and is pulled to the right by a horizontal force P. A small pulley is attached to the left face of collar B by a short horizontal bar. A cable is fixed to the wall at its upper end, runs horizontally to the right, wraps around the pulley on B and returns to the left to a second pulley that is mounted on the wall by a horizontal bracket (lower left). From this fixed pulley the cable hangs vertically down to block A of mass 1.5 kg.]
Q.5
-
Q.5 (A) 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.
[Figure: an incline rising to the right at 30° to the horizontal. A frictionless pulley is fixed at the upper end of the incline. Block A (lower on the incline) and block B (higher up) both rest on the incline. A rope from the upper side of A runs up parallel to the incline, over the pulley, and comes back down parallel to the incline to block B. Force P pulls A down the incline, parallel to it.]
-
Q.5 (B) 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 impulse momentum principle.
[Figure: crate on a horizontal floor, \(\mu_k = 0.3\); force P = 400 N pulls the crate to the right at 30° above the horizontal.]
Q.6
-
Q.6 (A) 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. Link 1 (length \(L_1\)) goes from O to joint A at angle \(\theta_1\) measured anticlockwise from \(X_0\). Link 2 (length \(L_2\)) goes from A to end point E; \(\theta_2\) is measured anticlockwise from the extension of link 1 (dashed line) to link 2.]
-
Q.6 (B) 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 D (x = 3 m), 3 m to B (x = 6 m), 1 m to E (x = 7 m), 2 m to the free end F (x = 9 m). Loads: 40 kN vertical downward at x = 2 m; a clockwise couple of 20 kN·m at the same point (x = 2 m); a triangular (uniformly varying) load increasing from zero at D to 24 kN/m (printed as “24 kNm”) at B; a vertical downward load P at E. No numerical value of P is printed in the paper.]