Part-A: Multiple Choice Questions

Choose the best answer andfill in the table provided with the secondfileyou downloaded.

Q1: Consider the motion of a body falling under gravity with air resistance included,        which is represented by the parameter k . The position of the body at any time is given by

y(t) =  −  (1− e− kt )

The dimension of the parameter [k] is given by

(A) [k] = T     (B) [k] = L /T      (C) [k] = T − 1         (D) [k] = L /T 2         (E) [k] = L− 1

Q2: With Planck’s constant h , the mass of the object m and the speed of light cone can construct a physical quantity  with length dimension. Using dimensional analysis,  is given by

(A)  =

(B)  =

(C)  =

(D)  =

(E) None of the above

Q3: Consider the following motion graphs for objects moving in 1D.

One (or more) of these graphs is (are) impossible, could you identify which.

(A) graph (a) only      (D) graphs (c) and (d)

(B) graphs (a) and (b)

(E) graphs (a) and (d)

(C) graphs (b) and (c)

For Q4 & Q5 refer to the following:

The graph to right corresponds to the velocity  , as a function of time, of

the subway train between Warden and Victoria Park stations. Assuming

that the motion was on a straight line, and the train started at time  = 0

from Warden station arriving at Victoria Park station, at time  =  . The

train departed with a constant acceleration  , and stars slowing down, at

time  = ! , with a constant acceleration  (with  < 0).

Q4:   In terms of the given parameters, the time !  can be written as

(A)  !  =             (B)   !  =          (C)   !  =  

(D)   !  =            (E) None of the above

Q5:  If the distance between the two stations is  , then the total time of the trip between Warden and Victoria Park stations is given by

2(β − α)                         2 α                    2 β  

Q6: Flight AC724 departed from Toronto heading north for a destination 800 km away. To fly directly and arriving in 2.0 hrs, the plane must be heading 20&  east of north. If the plane attains an airspeed of 500 km/hr, in Cartesian coordinates (with -axis pointing     north), the wind velocity vector (in km/h) is approximately given by

(A) v(!) = (− 171, --70)       (B) v(!) = (− 171, 70)       (C) v(!) = (171, --70)

(D) v(!) = (−70 , --171)        (E) None of the above

Q7: The diagram represents the straight-line motion of a car. Which of

the following statements is true?

(A) The car accelerates, stops, and reverses direction

(B) The car is moving for a total time of 12 s

(C) The car traveled largest distance while moving at constant speed.

(D) The car returns to its starting point when t = 9 s

(E) The car decelerates at 12 m/s2 for the last 4 s.

Q8: What value of lunch angle &  would cause the projectile’s maximum height to be   equal to 1/3 of its range? Assuming that, the projectile was fired from ground level with velocity & , making an angle &  above horizontal, and neglecting air resistance.  &  is      closest to

(A) θ0  = 300             (B) θ0  = 370               (C) θ0  = 530

(D) θ0  = 600             (E) None of the above

Q9: Which, if any, of the following systems (1 to 5) has (have) a constraint equation,     such that the magnitude of the acceleration  '  (of block 2) is twice the acceleration ( (of block 1) (i.e.,  !  = 2" )?

(A) Systems 3 & 5           (B) Systems 3            (C) Systems  5

(D) Systems 2 & 4           (E) No System

Q10:  The Figure to right shows two masses  ( &  '  and two pulleys ( &

'  connected by couple of ideal ropes, with tensions (  and ' , respectively.

The ratio of the tensions in the ropes is

(A) T1 / T2  = m1 / m2          (B) T1 / T2  = (m1 − m2 ) / (m1 + m2 )

(C) T1 / T2  = 1 / 2           (D) T1 / T2  = 1 / 4        (E) None of the above

Q11:  Let T represents the tension in the string,  is the net force and  is the           gravitational force exerted on the pendulum’s bob as it is swinging. The free body     diagram (FBD) for the bob of the pendulum, at its lowest point, is given by the graph

Q12: The two masses  ( and '  are connected by massless ropes and are

executing uniform circular motion with angular speed  , as shown in Fig.

to right. You may assume that the masses stay in the same horizontal

plane, and neglect gravity effect. Increasing the angular speed, which

string breaks first?

(A) The outer rope always breaks first.

(B) The inner rope always breaks first.

(C) The outer rope only breaks first when  (  >  ' .

(D) The outer rope only breaks first when  (  <  ' . (E) Both ropes always break at the same time.