AIEEE Mechanics Past year Question with Answers

1.A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement x is proportional to
A x²
B e^x
(C) x
(D) log_ex

Ans A



2.A ball is released from the top of a tower of height h metres. It takes T seconds to reach the ground. What is the position of the ball in T/3 seconds?
(A) h/9 metres from the ground
(B) 7h/9 metres from the ground
(C) 8h/9 metres from the ground
(D) 17h/18 metres from the ground.

Ans C.



3.A projectile can have the same range R for two angles of projection. If T₁ and T₂be the time of flights in the two cases, then the product of the two time of flights is directly proportional to
(A) 1/R²
(B) 1/R
(C) R
(D) R²

Ans C


4.Which of the following statements is false for a particle moving in a circle with a constant angular speed?
(A) The velocity vector is tangent to the circle.
(B) The acceleration vector is tangent to the circle.
(C) The acceleration vector points to the centre of the circle.
(D) The velocity and acceleration vectors are perpendicular to each other.

ANs B.


5.An automobile travelling with speed of 60 km/h, can brake to stop within a distance of 20 cm. If the car is going twice as fast, i.e 120 km/h, the stopping distance will be
(A) 20 m
(B) 40 m
(C) 60 m
(D) 80 m

ANs D.

6.A machine gun fires a bullet of mass 40 g with a velocity 1200 m/s. The man holding it can exert a maximum force of 144 N on the gun. How many bullets can he fire per second at the most?
(A) one
(B) four
(C) two
(D) three

Ans D.


7.A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, the motion of the particle takes place in a plane. It follows that
(A) its velocity is constant
(B) its acceleration is constant
(C) its kinetic energy is constant
(D) it moves in a straight line.

Ans C.

8. The relation between time t and distance x is t=ax²+bx where a and b are constants.
The acceleration is
(A) −2abv²
(B) 2bv³
(C) −2av³
(D) 2av²

Ans (C)

9. A particle located at x = 0 at time t = 0, starts moving along the positive x-direction with a velocity
‘v’ that varies as v = a x^1/2 . The displacement of the particle varies with time as
(A) t³
(B) t²
(C) t
(D) t^1/2

Ans: (B)

10. A bomb of mass 16 kg at rest explodes into two pieces of masses of 4 kg and 12 kg. The velocity
of the 12 kg mass is 4 m/s. The kinetic energy of the other mass is
(A) 96 J
(B) 144 J
(C) 288 J
(D) 192 J

Ans: (C)