String, pully and spring

A lot of problems in mechanics involves string, pulley and springs for example masses are attached to string or spring and so on. Here are some concepts you need to remember while solving problems involving string, spring and pulleys.
(1) String
A. If not staded in the question consider the string to be inextensible.
B. Different blocks connected to an inextensible string would have same acceleration and for extensible string blocks would have different acceleration until the string can stretch.
C. Unless otherwise specified consider the string to be light i.e., consider its mass to be negligible in comparison to the block connected to it.
D. For a massless string tension in the string is zero although an ideal massless string is an practical impossibility.
E. Tension on different parts of the string would be different if string possess a considerable mass.

(2) Pulley
A. Unless or otherwise specified consider the pulley to be light having no effect on the system due to its weight.
B. The tension on strion on either side of pulley is taken to be same
C. If not specified consider the oulley to be frictionless in nature.

(3) Spring
A. Unless or otherwise specified consider the spring to be light and force constant of spring is same throughout whole length of the spring.
B. Spring has a elastic property that it can be compressed and stretched easily.
C. To stretch or compress a spring equal and opposite forces have to be applied at both the ends of the spring and in responce spring apply equal and opposite restoring force to bring the spring back to its natural position.
D For small compression and elongations this restoring force is given by Hook's Law which is
F=kx
where k is the spring constant and x is elongation or compression from the natural length of the spring.

So keep solving more and more physics problems Keeping these facts in mind. All the very best for your exams.

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)