EM Practice questions set with answers for class test-II_2023-24

 

(Q.2)  The acceleration of the particle is defined by the relation a = 25 - 3x² mm/s². The particle starts with no initial velocity at the position x = 0. (a) Determine the velocity when x = 2 mm (b) the position when velocity is again zero, (c) position where the velocity is maximum and the corresponding maximum velocity.

(Q.3)  Acceleration of a particle moving along a straight line is represented by the relation a = 30 - 4.5x² m/s². The particle starts with zero initial velocity at x = 0. Determine (a) The velocity when x = 3 m, (b) the position when the velocity is again zero (c) the position when the velocity is maximum.

Solution: 

(Q.6)  A stone is dropped from the top of a tower. When it has fallen a distance of 10m, another stone is dropped from a point 38 m below the top of the tower. If both the stones reach the ground at the same time calculate (i) the height of the tower (ii) the velocity of the stones when they reach the ground.

(Q.7)   From (v-t) diagram find (i) distance travelled in 10sec. (ii) total distance travelled in 50 sec.

(iii) Retardation.

(Q.7)   From (v-t) diagram find (i) distance travelled in 10sec. (ii) total distance travelled in 50 sec    (iii) Retardation.

(Q.8)   The race car starts from rest and travels along a straight road until it reaches a   speed of 42m/s in 50 seconds as shown by v-t graph. Determine the distance travelled by race car      in 50 seconds. Draw x-t and a-t graph.

(Q.13) A ball is projected from the top of tower 110 m height with the velocity of 100 m/s at an angle of 25° to the horizontal. Neglecting the air resistance, find (1) The maximum height the ball will rise from the ground, (2) The horizontal distance it will travel before it strikes the ground, (3) The velocity with which it strikes the ground.

Solution: 

(Q.14)   An aero plane is flying in horizontal direction with a velocity of 540 km/hr and at height of 2200m. When it is vertically above the point A on the ground, an object is dropped from it. The object strikes the ground at point B. Calculate the distance AB (ignore air resistance). Also find velocity at B and time taken to reach B. 

(Q.20) Figure shows a collar B which moves up with constant velocity of 2 m/ s. To the collar is pinned a rod AB, the end A of which slides freely against a 30° sloping ground. For this instant, determine the angular velocity of the rod and velocity of end A of the rod.

Solution:

i)               In triangle IAB, using sign rule

 

    1.5            IA           IB

-------- = --------- = ------- 

 Sin 60⁰      sin 50⁰      sin70⁰

 

IA = 1.326 m/s      and       IB = 1.628 m/s

ii)             Rod AB performs general plane motion

 

                      V_B = (IB) x (ω_AB)

                 (ω_AB) = V_B / (IB)

                           = 2 / 1.628

                           = 1.23 rad/sec

                     V_A = (IA) x (ω_AB)

                           = 1.326 x 1.23

                           = 1.63 m/s

 

               In triangle ICB,

                 (IC)² = (IB)² + (BC)² – 2(IB)(CB)cos40⁰

                         = (1.628)² + (0.75)² – 2(1.628)(0.75)cos40⁰

                         = √(1.342)

                         = 1.158 m

                   Vc = IC x (ω_AB)

                        = 1.158 x 1.23

                        = 1.425 m/s