University of Mumbai 2007-1st Sem B.E FE Engg Mechanics - exam paper

B (IJ Question No. 1 is compulsory.

(2)    Attempt any four questions out of remaining six questions.

(3)    Assume suitable data if necessary and mention them clearly. fY)Cl$

(4)    Take g = 9-81 m/s2.    j    ~

/inn * '    *    1 '

Solve any four of folfowing : J    )

(a) Resolve a system of forces shown in figure into a force and couple at point *A\

(b) A force R = 25 N has components F_a, F_b and F_c as shown in figure. If F_c = 20 N.

Find F_a and F_b.

(c)    Derive an expression for the Moment of Inertia of a rectangle about its centroidal Y-axis.

(d)    State and prove Work-Energy principle.

(e)    Water leaks from the ceiling 16 m high, at the rate of 5 drops per second. Find the distance between first and second drop when the first drop has just touched the ground.

(f)    Find distance V so that the CG of given area in figure has co-ordinates (25, 20).

Determine using fundamentals, the maximum height reached and the maximum distance 10 travelled on horizontal surface by a projectile fired with velocity of 25 m/s at an angle of 40^u. Derive expression for maximum height and maximum distance on horizontal surface and verify your answers.

Find Momen't of inertia of given area about centroidal X and Y axis. Refer figure.    10

3. (a) Find forces in ail the members of the truss shown in figure. Afso find support reactions. 10 Use method of sections for any three members.

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connected at pointDto maintain the shown position ?

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* * from rest. Mass of block A, B and C is 5 kg, 10 kg and 50 kg respectively. Co-efficient of friction for block A and B is 0-3. Neglect weight of pulley and rope friction.

(b) Determine minimum value of co-efficient of frictiop so as to maintain the position shown 10 in figure. Length of Rod AB is 3-5 m and it weighs 250 N.

r

(a) Find the velocity of block A and B when block A has travelled 1 *2 m along inclined plane. Mass of A is 10 kg and that of B is 50 kg. coefficient of friction between block A and inclined plane is 0-25. Pulley are mass less and frictionless. Use work energy principle.

6.    (a) Explain what is coefficient of restitution. A tennis ball of 75 gm mass falls on ground through 10

a height of 3 m. How many times it will bounce before it comes to rest ? Take e = 0-7.

(b) Acceleration of particle is directly proportional to the square of time T. When t = 0, 10 particle is at x = 24 m. Knowing that at t = 6 sec, x = 96 m and v = 18 m/s. Find expressions of x and v in terms of t. Also find velocity and position aft = 2 sec.

7.    (a) Prove that    10

(i)    Moment of area of a-t curve gives displacement.

(ii)    Area under a-t curve gives velocity

(iii)    Area under v-t curve gives displacement.

(b) Two wheels are attached to the ends of rod AB as shown in figure. Find the angular 10 velocity of the rod in terms of V_b, L, a and 0.

Vo. A
B

Attachment: university-of-mumbai-2007-b-e-50939-1.pdf

Earning:   Approval pending.